mathematics 1 - ade/fyco - 2019/2020 list of exercises 03...
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Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 1530
Exercise 1
Compute 3 a
0
(-3 a + 2 t - 18 a t + 9 t2 - 36 a t2 + 16 t3)ⅆt
1) The rest of the solutions are not correct
2) -3 - 15 a
3) -1 - 14 a
4) -10 - 4 a
5) 2 - 13 a
6) 10 - 5 a
Exercise 2
Compute -1
2
((-2 + 6 t) Cos[3 + 2 t])ⅆt
1) 6.97122
2) 3.32971
3) -31.1912
4) -23.7129
5) 0.524269
6) -22.7851
Exercise 3
Compute 3
8
(24
(2 + 2 t)2)ⅆt
1) -3.26845
2) -5320.
3) -3.18184
4) -3.40154
5) 0.833333
6) -4.47428
Exercise 4
Compute 3
5 6 a + t - 3 a t
-2 t + t2ⅆt
1) The rest of the solutions are not corret
2) -3 a Log5
3 - Log[9]
3) -a Log25
9 - 4 Log[3]
4) 5 a Log5
3 - Log[3]
5) -3 a Log5
3 + Log[3]
6) -3 a Log5
3 + Log[3]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(1 + 5 t)ⅇ-1+2 t millions of euros/year.
If the initial deposit in the investment fund was 90
millions of euros, compute the depositis available after 3 years.
1) 90 +3
4 ⅇ+27 ⅇ5
4millions of euros = 1092.0647 millions of euros
2) 90 -13
4 ⅇ3+
3
4 ⅇmillions of euros = 90.1141 millions of euros
3) 90 +3
4 ⅇ+17 ⅇ3
4millions of euros = 175.6394 millions of euros
4) 90 +3
4 ⅇ+7 ⅇ
4millions of euros = 95.0329 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(6 + t)ⅇ3+3 t euros.
Compute the average value of the shares along the first
8 months of the year (between t=0 and t=8).
1)1
8-17 ⅇ3
9+23 ⅇ9
9euros = 2583.7427 euros
2)1
8-17 ⅇ3
9+20 ⅇ6
9euros = 107.3211 euros
3)1
8
14
9-17 ⅇ3
9euros = -4.548 euros
4)1
8-17 ⅇ3
9+41 ⅇ27
9euros = 3.0297×1011 euros
2
Exercise 7Compute the area enclosed by the function f(x)=-12 x + 10 x2 - 2 x3
and the horizontal axis between the points x=-1 and x=5.
1) 36
2) 45
3)178
3= 59.3333
4)172
3= 57.3333
5)365
6= 60.8333
6)181
3= 60.3333
7)359
6= 59.8333
8)167
3= 55.6667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(2 - t
2441310)ⅇ
3+3 t per-unit.
The initial deposit in the account is 5000 euros. Compute the deposit after 3 years.
1) 5016.44 euros
2) 4976.44 euros
3) 4926.44 euros
4) 4956.44 euros
3
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 339599
Exercise 1
Compute -a
1
(-15 - a - 2 t - 14 a t - 21 t2 + 9 a t2 + 12 t3)ⅆt
1) 11 - 12 a
2) The rest of the solutions are not correct
3) -20 (1 + a)
4) 1 - 12 a
5) 12 - 11 a
6) -1 - 13 a
Exercise 2
Compute 0
1
(12 + 8 t - 12 t2 Cos[2 + 2 t])ⅆt
1) -10.0344
2) -39.7655
3) -7.84372
4) -4.54081
5) -46.6205
6) -43.4878
Exercise 3
Compute 3
5
(-486
(2 - 3 t)5)ⅆt
1) -4.64606
2) -3.3917
3) -1.17729×106
4) -4.33386
5) 0.01545
6) -3.96291
4
Exercise 4
Compute -1
2 4 - 6 a + 2 t - 2 a t
6 + 5 t + t2ⅆt
1) -a Log[4] + Log25
4
2) -5 a Log[4] - 4 Log[5] + Log[16]
3) -2 a Log[4] + Log25
4
4) The rest of the solutions are not corret
5) 4 Log5
2 + a Log[4]
6) 3 Log5
2 - a Log[4]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=20 ⅇ-3+t millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 1 year.
1) 60 -20
ⅇ3millions of euros = 59.0043 millions of euros
2) 40 -20
ⅇ3+20
ⅇ2millions of euros = 41.711 millions of euros
3) 40 +20
ⅇ4-20
ⅇ3millions of euros = 39.3706 millions of euros
4) 40 -20
ⅇ3+20
ⅇmillions of euros = 46.3618 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=10 ⅇ2+t euros.
Compute the average value of the shares along the first
4 months of the year (between t=0 and t=4).
1)1
410 ⅇ - 10 ⅇ
2 euros = -11.6769 euros
2)1
4-10 ⅇ
2+ 10 ⅇ
6 euros = 990.0993 euros
3)1
4-10 ⅇ
2+ 10 ⅇ
3 euros = 31.7412 euros
4)1
4-10 ⅇ
2+ 10 ⅇ
4 euros = 118.0227 euros
5
Exercise 7Compute the area enclosed by the function f(x)=-12 - 10 x - 2 x2
and the horizontal axis between the points x=-4 and x=1.
1) 31
2) 25
3) 29
4)61
2= 30.5
5)63
2= 31.5
6)77
3= 25.6667
7) 32
8)65
2= 32.5
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
11ⅇ-2+2 t per-unit.
The initial deposit in the account is 1000 euros. Compute the deposit after 1 year.
1) 1100.0855 euros
2) 1040.0855 euros
3) 1090.0855 euros
4) 1020.0855 euros
6
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 453722
Exercise 1
Compute a
-5
(3 - 4 a + 8 t + 10 a t - 15 t2 + 6 a t2 - 8 t3)ⅆt
1) -10 - 6 a
2) 2 a
3) 4 a
4) The rest of the solutions are not correct
5) 10 - 6 a
6) 5 - 8 a
Exercise 2
Compute 0
1
(-3 Sin[3 - 2 t])ⅆt
1) -0.810453
2) -9.24516
3) -7.90588
4) -11.177
5) -2.29544
6) -8.6834
Exercise 3
Compute 3
8
(16
-5 + 4 t)ⅆt
1) -20.4265
2) -26.2923
3) -21.7479
4) -18.5975
5) 1.34993
6) 5.39971
7
Exercise 4
Compute 4
5 2 - 3 a - t + a t
6 - 5 t + t2ⅆt
1) The rest of the solutions are not corret
2) -4 a Log3
2 + Log[2]
3) 4 a Log3
2 + Log[2]
4) Log[2] - a Log9
4
5) 5 a Log3
2 - 5 Log[2]
6) -5 Log[2] + a Log9
4
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=1 + t + t3 millions of euros/year.
If the initial deposit in the investment fund was 70
millions of euros, compute the depositis available after 1 year.
1)287
4millions of euros = 71.75 millions of euros
2) 146 millions of euros
3) 78 millions of euros
4)391
4millions of euros = 97.75 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(2 + 4 t)(sin(2πt)+2) euros.
Compute the average value of the shares along the first
5 months of the year (between t=0 and t=5).
1)2
5 πeuros = 0.1273 euros
2)1
58 -
2
πeuros = 1.4727 euros
3)1
5120 -
10
πeuros = 23.3634 euros
4)1
524 -
4
πeuros = 4.5454 euros
8
Exercise 7Compute the area enclosed by the function f(x)=
-6 + 5 x - x2 and the horizontal axis between the points x=-2 and x=2.
1)197
6= 32.8333
2)185
6= 30.8333
3)203
6= 33.8333
4)94
3= 31.3333
5)88
3= 29.3333
6)100
3= 33.3333
7)97
3= 32.3333
8)191
6= 31.8333
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(2 + 4 t))(sin(2πt)+2) per-unit.
The initial deposit in the account is 18 000 euros. Compute the deposit after 4 years.
1) 39112.5028 euros
2) 39072.5028 euros
3) 39092.5028 euros
4) 39052.5028 euros
9
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 4829387
Exercise 1
Compute -3 a
4
(9 a + 6 t - 60 a t - 30 t2 + 27 a t2 + 12 t3)ⅆt
1) -11 - 13 a
2) 44 (4 + 3 a)
3) The rest of the solutions are not correct
4) -8 - 7 a
5) 1 - 5 a
6) -6 - 13 a
Exercise 2
Compute -3
0
(-2 Cos[2 - 3 t])ⅆt
1) -1.99998
2) -6.27068
3) -5.9854
4) -5.36038
5) 1.27286
6) -0.0265542
Exercise 3
Compute 1
9
(54
(-1 + 3 t)2)ⅆt
1) 8.30769
2) -39.0655
3) -17 568.
4) -27.0988
5) -40.9274
6) -34.9861
10
Exercise 4
Compute 5
7 9 - 3 t - 2 a t
-3 t + t2ⅆt
1) -Log7
5 - a Log[4]
2) 3 Log7
5 + a Log[2]
3) -Log343
125 - a Log[4]
4) -5 Log7
5 - a Log[2]
5) -5 a Log[2] + Log343
125
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=30 ⅇ-1+2 t millions of euros/year.
If the initial deposit in the investment fund was 80
millions of euros, compute the depositis available after 1 year.
1) 80 -15
ⅇ+ 15 ⅇ
3 millions of euros = 375.7649 millions of euros
2) 80 -15
ⅇ+ 15 ⅇ
5 millions of euros = 2300.6792 millions of euros
3) 80 -15
ⅇ+ 15 ⅇ millions of euros = 115.256 millions of euros
4) 80 +15
ⅇ3-15
ⅇmillions of euros = 75.2286 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(4 + 2 t)log(3 t) euros.
Compute the average value of shares between month 1 and month 3 (between t=1 and t=3).
1)1
2-39
2- 5 Log[3] + 32 Log[12] euros = 27.262 euros
2)1
3(-28 - 5 Log[3] + 45 Log[15]) euros = 29.4564 euros
3)1
3-39
2- 5 Log[3] + 32 Log[12] euros = 18.1747 euros
4)1
2(-12 - 5 Log[3] + 21 Log[9]) euros = 14.3243 euros
11
Exercise 7Compute the area enclosed by the function f(x)=-12 x - 2 x2 + 2 x3
and the horizontal axis between the points x=-5 and x=5.
1)1234
3= 411.3333
2)1228
3= 409.3333
3) 325
4)500
3= 166.6667
5)1237
3= 412.3333
6)2471
6= 411.8333
7)1039
3= 346.3333
8)2465
6= 410.8333
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(3 + 4 t))log(5 t) per-unit.
In the year t=1 we deposint in the account 13 000
euros. Compute the deposit in the account after (with respect to t=1) 4 years.
1) 67792.5139 euros
2) 67812.5139 euros
3) 67832.5139 euros
4) 67842.5139 euros
12
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 7404309
Exercise 1
Compute 2 a
4
(6 + 4 a - 4 t + 24 a t - 18 t2 - 12 a t2 + 8 t3)ⅆt
1) 6 - 2 a
2) 7 - 7 a
3) 11 - 7 a
4) The rest of the solutions are not correct
5) 1 - 11 a
6) -7 - 11 a
Exercise 2
Compute 0
1
(ⅇ1+3 t
9 + 27 t + 9 t2)ⅆt
1) 1392.25
2) -2777.4
3) 580.568
4) -1929.86
5) 464.084
6) -2634.85
Exercise 3
Compute -8
-7
(28
(-2 + 2 t)2)ⅆt
1) -1736.
2) -4.78393
3) -4.5384
4) -3.26757
5) -3.32408
6) 0.0972222
13
Exercise 4
Compute 4
6 -15 + 5 t - 4 a t
-3 t + t2ⅆt
1) The rest of the solutions are not corret
2) -5 Log3
2 - a Log[9]
3) -4 Log3
2 + 5 a Log[3]
4) -Log3
2 + 5 a Log[3]
5) Log243
32 - a Log[81]
6) 5 Log3
2 + a Log[3]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(2 + 2 t)(cos(2πt)+2) millions of euros/year.
If the initial deposit in the investment fund was 70
millions of euros, compute the depositis available after 5 years.
1) 140 millions of euros
2) 76 millions of euros
3) 68 millions of euros
4) 86 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(3 + 2 t)log(3 t) euros.
Compute the average value of shares between month 1 and month 2 (between t=1 and t=2).
1) -9
2- 4 Log[3] + 10 Log[6] euros = 9.0231 euros
2) -10 - 4 Log[3] + 18 Log[9] euros = 25.1556 euros
3)1
2(-10 - 4 Log[3] + 18 Log[9]) euros = 12.5778 euros
4)1
2-33
2- 4 Log[3] + 28 Log[12] euros = 24.3415 euros
14
Exercise 7Compute the area enclosed by the function f(x)=
-3 x + x2 and the horizontal axis between the points x=-4 and x=2.
1)158
3= 52.6667
2) 42
3)152
3= 50.6667
4)155
3= 51.6667
5)307
6= 51.1667
6)146
3= 48.6667
7)313
6= 52.1667
8)301
6= 50.1667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(3 + 2 t))log(t) per-unit.
In the year t=1 we deposint in the account 2000
euros. Compute the deposit in the account after (with respect to t=1) 3 years.
1) 2570.0472 euros
2) 2500.0472 euros
3) 2490.0472 euros
4) 2550.0472 euros
15
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 7511795
Exercise 1
Compute -3 a
2
(-9 a - 6 t - 12 a t - 6 t2 - 18 a t2 - 8 t3)ⅆt
1) -1 - 3 a
2) The rest of the solutions are not correct
3) -30 (2 + 3 a)
4) 10 - 15 a
5) -12 - 10 a
6) -12 - 12 a
Exercise 2
Compute 0
1
((9 - 6 t) Cos[3 t])ⅆt
1) 0.28224
2) -5.73826
3) -3.11797
4) -5.93995
5) 1.46778
6) -6.16946
Exercise 3
Compute 6
8
(4
t3)ⅆt
1) -3.90948
2) -4.20326
3) -2.12428
4) -1.81173
5) 0.0243056
6) -22 400.
16
Exercise 4
Compute 4
5 12 - 4 t + 4 a t
-3 t + t2ⅆt
1) -4 Log5
4 - 5 a Log[2]
2) The rest of the solutions are not corret
3) -a Log[2] - 2 Log[5] + Log[16]
4) -5 Log5
4 + a Log[8]
5) a Log[2] + Log625
256
6) -4 Log5
4 + a Log[16]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(4 + 5 t)(sin(2πt)+1) millions of euros/year.
If the initial deposit in the investment fund was 50
millions of euros, compute the depositis available after 2 years.
1) 68 -5
πmillions of euros = 66.4085 millions of euros
2)97
2+
5
2 πmillions of euros = 49.2958 millions of euros
3)169
2-
15
2 πmillions of euros = 82.1127 millions of euros
4)113
2-
5
2 πmillions of euros = 55.7042 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(4 + 2 t)log(4 t) euros.
Compute the average value of shares between month 1 and month 3 (between t=1 and t=3).
1)1
3(-28 - 5 Log[4] + 45 Log[20]) euros = 33.2922 euros
2)1
2(-12 - 5 Log[4] + 21 Log[12]) euros = 16.6258 euros
3)1
2-39
2- 5 Log[4] + 32 Log[16] euros = 31.1457 euros
4)1
3-39
2- 5 Log[4] + 32 Log[16] euros = 20.7638 euros
17
Exercise 7Compute the area enclosed by the function f(x)=-12 x - 2 x2 + 2 x3
and the horizontal axis between the points x=-5 and x=3.
1)896
3= 298.6667
2)902
3= 300.6667
3)643
3= 214.3333
4)905
3= 301.6667
5)832
3= 277.3333
6)1807
6= 301.1667
7)707
3= 235.6667
8)1813
6= 302.1667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(4 + 2 t))log(5 t) per-unit.
In the year t=1 we deposint in the account 14 000
euros. Compute the deposit in the account after (with respect to t=1) 4 years.
1) 41557.5642 euros
2) 41537.5642 euros
3) 41607.5642 euros
4) 41627.5642 euros
18
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 7572959
Exercise 1
Compute -3 a
3
(-6 a - 4 t + 6 a t + 3 t2 - 27 a t2 - 12 t3)ⅆt
1) -2 - a
2) 13 - 3 a
3) The rest of the solutions are not correct
4) -3 - 12 a
5) -2 - 14 a
6) -234 (1 + a)
Exercise 2
Compute -2
1
((3 - 9 t) Cos[3 - 3 t])ⅆt
1) -4.82583
2) -4.92376
3) -4.76234
4) 0.973699
5) -3.29695
6) -23.3671
Exercise 3
Compute 3
6
(36
(-1 - 3 t)2)ⅆt
1) -4.53304
2) 5859.
3) 0.568421
4) -4.92376
5) -4.76234
6) -4.82583
19
Exercise 4
Compute 4
5 -12 - 3 a + 4 t - a t
-9 + t2ⅆt
1) -Log8
7 - 4 a Log[2]
2) -a Log[2] - 4 Log[7] + 4 Log[8]
3) Log8
7 + a Log[2]
4) 2 Log8
7 + a Log[4]
5) The rest of the solutions are not corret
6) -2 Log8
7 + a Log[4]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=t + t2 + 3 t3 millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 2 years.
1)170
3millions of euros = 56.6667 millions of euros
2)499
12millions of euros = 41.5833 millions of euros
3)784
3millions of euros = 261.3333 millions of euros
4)457
4millions of euros = 114.25 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(4 + 4 t + 3 t2)log(t) euros.
Compute the average value of shares between month 1 and month 3 (between t=1 and t=3).
1)1
2-74
3+ 57 Log[3] euros = 18.9771 euros
2)1
2(-48 + 112 Log[4]) euros = 53.6325 euros
3)1
3-244
3+ 195 Log[5] euros = 77.5024 euros
4)1
3(-48 + 112 Log[4]) euros = 35.755 euros
20
Exercise 7Compute the area enclosed by the function f(x)=-18 + 18 x + 2 x2 - 2 x3
and the horizontal axis between the points x=-3 and x=5.
1)512
3= 170.6667
2) 0
3)601
3= 200.3333
4)1199
6= 199.8333
5)1193
6= 198.8333
6)598
3= 199.3333
7)604
3= 201.3333
8)592
3= 197.3333
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(4 + 4 t))log(t) per-unit.
In the year t=1 we deposint in the account 3000
euros. Compute the deposit in the account after (with respect to t=1) 4 years.
1) 6274.1525 euros
2) 6264.1525 euros
3) 6204.1525 euros
4) 6254.1525 euros
21
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 7684103
Exercise 1
Compute 3 a
-2
(-6 - 9 a + 6 t - 48 a t + 24 t2 + 36 a t2 - 16 t3)ⅆt
1) The rest of the solutions are not correct
2) -12 - 8 a
3) 4 - 7 a
4) -7 - 11 a
5) -7 - 2 a
6) -52 (2 + 3 a)
Exercise 2
Compute 0
1
(12 - 12 t + 12 t2 Sin[2 t])ⅆt
1) -29.115
2) 9.09297
3) 2.08073
4) -24.9221
5) -33.2067
6) 6.97633
Exercise 3
Compute 4
5
(8
-4 + 2 t)ⅆt
1) 1.62186
2) -6.76866
3) 0.405465
4) -7.71991
5) -5.7939
6) -5.25219
22
Exercise 4
Compute 5
7 8 + 15 a - 4 t - 5 a t
6 - 5 t + t2ⅆt
1) The rest of the solutions are not corret
2) -3 a Log5
3 - Log[2]
3) 5 a Log5
3 + Log[2]
4) -5 a Log5
3 - Log[4]
5) Log[4] + a Log125
27
6) Log[2] - a Log25
9
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(1 + 4 t)log(3 t) millions of euros/year.
If, for t=1, the deposits in the investment fund were 90
millions euros, compute the deposit available after (with respect to t=1) 3 years.
1) 50 - 3 Log[3] + 78 Log[18] millions of euros = 272.1532 millions of euros
2) 62 - 3 Log[3] + 55 Log[15] millions of euros = 207.6469 millions of euros
3) 122 - 3 Log[3] + 36 Log[12] millions of euros = 208.1608 millions of euros
4) 72 - 3 Log[3] + 36 Log[12] millions of euros = 158.1608 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(3 + 4 t)(cos(2πt)+1) euros.
Compute the average value of the shares along the first
7 months of the year (between t=0 and t=7).
1) -1
7euros = -0.1429 euros
2) 2 euros
3) 17 euros
4)5
7euros = 0.7143 euros
23
Exercise 7Compute the area enclosed by the function f(x)=-6 + 11 x - 6 x2 + x3
and the horizontal axis between the points x=-5 and x=0.
1)2305
4= 576.25
2)2301
4= 575.25
3)2303
4= 575.75
4)2295
4= 573.75
5)2311
4= 577.75
6)2307
4= 576.75
7)2313
4= 578.25
8)2315
4= 578.75
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(3 + 4 t))(cos(2πt)+2) per-unit.
The initial deposit in the account is 6000 euros. Compute the deposit after 2 years.
1) 7958.7789 euros
2) 7938.7789 euros
3) 7978.7789 euros
4) 7998.7789 euros
24
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 8463511
Exercise 1
Compute a
-5
(-3 - 14 a + 28 t - 28 a t + 42 t2 - 9 a t2 + 12 t3)ⅆt
1) The rest of the solutions are not correct
2) 15 - 11 a
3) 98 (5 + a)
4) -9 - 15 a
5) -7 - 11 a
6) 3 - 11 a
Exercise 2
Compute 2
3
(Log[t])ⅆt
1) 0.909543
2) 2.11492
3) -4.60287
4) 1.90954
5) -4.54819
6) -3.01719
Exercise 3
Compute 5
8
(1
3 + t)ⅆt
N: Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating -Log11
8 - Log[8] + Log[11].
1) -3.01719
2) -2.77021
3) -2.5885
4) -4.54819
5) -4.60287
6) 0.318454
25
Exercise 4
Compute 1
2 -3 a - t - a t
3 t + t2ⅆt
1) Log5
4 - a Log[4]
2) -Log5
4 - a Log[2]
3) The rest of the solutions are not corret
4) -3 Log5
4 + a Log[2]
5) -4 Log5
4 - a Log[8]
6) -4 Log5
4 - a Log[4]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=2 t2 + t3 millions of euros/year.
If the initial deposit in the investment fund was 80
millions of euros, compute the depositis available after 1 year.
1)971
12millions of euros = 80.9167 millions of euros
2)473
4millions of euros = 118.25 millions of euros
3)560
3millions of euros = 186.6667 millions of euros
4)268
3millions of euros = 89.3333 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(1 + 6 t)ⅇ-2+t euros.
Compute the average value of the shares along the first
9 months of the year (between t=0 and t=9).
1)1
97 +
5
ⅇ2euros = 0.853 euros
2)1
9
5
ⅇ2+ 49 ⅇ
7 euros = 5970.6335 euros
3)1
9-11
ⅇ3+
5
ⅇ2euros = 0.0143 euros
4)1
9
5
ⅇ2+1
ⅇeuros = 0.1161 euros
26
Exercise 7Compute the area enclosed by the function f(x)=-18 x - 15 x2 - 3 x3
and the horizontal axis between the points x=-5 and x=-1.
1) 60
2) 64
3)133
2= 66.5
4)139
2= 69.5
5)115
2= 57.5
6) 69
7) 68
8)137
2= 68.5
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
16(-1 - t))ⅇ-1+t per-unit.
The initial deposit in the account is 1000 euros. Compute the deposit after 1 year.
1) 999.4131 euros
2) 1009.4131 euros
3) 919.4131 euros
4) 939.4131 euros
27
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 26522947
Exercise 1
Compute -3 a
2
(15 a + 10 t - 24 a t - 12 t2 - 45 a t2 - 20 t3)ⅆt
1) The rest of the solutions are not correct
2) 11 + 4 a
3) 14 - 3 a
4) -13 + 3 a
5) -13 - 3 a
6) -46 (2 + 3 a)
Exercise 2
Compute 0
1
(-4 - 8 t + 4 t2 Sin[2 t])ⅆt
1) -4.20056
2) -3.65355
3) -0.583853
4) -3.95722
5) -1.2124
6) -0.277431
Exercise 3
Compute 0
8
(-96
(-2 - 2 t)5)ⅆt
1) -3.65355
2) 0.749886
3) -8.50304×106
4) -3.95722
5) -2.86945
6) -4.20056
28
Exercise 4
Compute 3
4 -8 + 5 a - 4 t - 5 a t
-2 + t + t2ⅆt
1) -5 a Log6
5 - Log
81
16
2) -3 a Log6
5 + Log
3
2
3) 4 a Log6
5 + Log
3
2
4) The rest of the solutions are not corret
5) 3 a Log6
5 + Log
3
2
6) -a Log6
5 + Log
9
4
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(1 + 4 t + 4 t2)log(2 t) millions of euros/year.
If, for t=1, the deposits in the investment fund were 50
millions euros, compute the deposit available after (with respect to t=1) 5 years.
1) -410
9-13 Log[2]
3+ 366 Log[12] millions of euros = 860.9166 millions of euros
2) -770
9-13 Log[2]
3+ 366 Log[12] millions of euros = 820.9166 millions of euros
3) 4 -13 Log[2]
3+364 Log[8]
3millions of euros = 253.3019 millions of euros
4) -298
9-13 Log[2]
3+665 Log[10]
3millions of euros = 474.2916 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=30 ⅇ2+t euros.
Compute the average value of the shares along the first
7 months of the year (between t=0 and t=7).
1)1
7-30 ⅇ
2+ 30 ⅇ
4 euros = 202.3247 euros
2)1
7-30 ⅇ
2+ 30 ⅇ
9 euros = 34695.8352 euros
3)1
7-30 ⅇ
2+ 30 ⅇ
3 euros = 54.4135 euros
4)1
730 ⅇ - 30 ⅇ
2 euros = -20.0176 euros
29
Exercise 7Compute the area enclosed by the function f(x)=6 - 5 x - 2 x2 + x3
and the horizontal axis between the points x=-5 and x=2.
1)1757
12= 146.4167
2)2171
12= 180.9167
3)1699
12= 141.5833
4)2165
12= 180.4167
5)2077
12= 173.0833
6)2177
12= 181.4167
7)2159
12= 179.9167
8)2135
12= 177.9167
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=ⅇ-3+t
14per-unit.
The initial deposit in the account is 20 000 euros. Compute the deposit after 3 years.
1) 21444.5737 euros
2) 21474.5737 euros
3) 21404.5737 euros
4) 21414.5737 euros
30
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 45942139
Exercise 1
Compute 3 a
-1
(-2 - 15 a + 10 t - 30 a t + 15 t2 - 9 a t2 + 4 t3)ⅆt
1) The rest of the solutions are not correct
2) -3 - 8 a
3) 1 - a
4) 14 - 15 a
5) 3 + 9 a
6) -1 + 6 a
Exercise 2
Compute -3
-1
(3 Cos[1 + t])ⅆt
1) -8.98978
2) -6.74532
3) 2.72789
4) -11.1412
5) -8.18368
6) -9.39592
Exercise 3
Compute 3
4
(30
2 + 5 t)ⅆt
1) 0.257829
2) -6.31811
3) 1.54697
4) -5.04451
5) -5.09806
6) -5.32838
31
Exercise 4
Compute 4
7 1 + 9 a + t - 3 a t
-3 - 2 t + t2ⅆt
1) The rest of the solutions are not corret
2) -3 a Log8
5 - 2 Log[4]
3) -a Log8
5 - 3 Log[4]
4) 2 -2 a Log8
5 + Log[4]
5) -3 a Log8
5 + Log[4]
6) 5 -a Log8
5 + Log[4]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(8 + 9 t)ⅇ3 t millions of euros/year.
If the initial deposit in the investment fund was 70
millions of euros, compute the depositis available after 1 year.
1)205
3-
4
3 ⅇ3millions of euros = 68.267 millions of euros
2)205
3+32 ⅇ9
3millions of euros = 86501.2286 millions of euros
3)205
3+23 ⅇ6
3millions of euros = 3161.2874 millions of euros
4)205
3+14 ⅇ3
3millions of euros = 162.0658 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=cos(6 + 6 t) euros.
Compute the average value of the shares along the first
2 π months of the year (between t=0 and t=2 π).
1)-Sin[6]
6+
1
6Sin[6 (1 + 2 π)]
2 πeuros = 0. euros
2)-Sin[6]
6+
1
6Sin[6 (1 + 2 π)]
2 πeuros = 0. euros
3) 80 +
-Sin[6]
6+
1
6Sin[6 (1 + 2 π)]
2 πeuros = 80. euros
4) 20 +
-Sin[6]
6+
1
6Sin[6 (1 + 2 π)]
2 πeuros = 20. euros
32
Exercise 7Compute the area enclosed by the function f(x)=-18 - 18 x + 2 x2 + 2 x3
and the horizontal axis between the points x=-5 and x=0.
1)743
6= 123.8333
2)725
6= 120.8333
3)370
3= 123.3333
4)737
6= 122.8333
5)367
3= 122.3333
6)565
6= 94.1667
7)619
6= 103.1667
8)153
2= 76.5
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
10cos(-5 + 9 t) per-unit.
The initial deposit in the account is 7000 euros. Compute the deposit after 4 π years.
1) 6980 euros
2) 7000 euros
3) 6997.901 euros
4) 7010 euros
33
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 46272561
Exercise 1
Compute 3 a
4
(-12 + 12 a - 8 t + 36 a t - 18 t2 + 18 a t2 - 8 t3)ⅆt
1) 12 - 5 a
2) The rest of the solutions are not correct
3) -6 - 14 a
4) 252 (-4 + 3 a)
5) -9 - 14 a
6) -3 - 13 a
Exercise 2
Compute 0
1
(4 + 12 t + 8 t2 Cos[2 + 2 t])ⅆt
1) -4.79308
2) -8.27949
3) -10.8951
4) -47.5846
5) -49.8276
6) -47.6986
Exercise 3
Compute 2
8
(-1
(1 - t)5)ⅆt
1) -3.87984
2) 0.249896
3) -4.5734
4) -29 412.
5) -4.37799
6) -4.36753
34
Exercise 4
Compute 3
4 -10 + 4 a + 5 t + 2 a t
-4 + t2ⅆt
1) 2 Log6
5 + a Log[4]
2) a Log[4] - 5 Log[5] + 5 Log[6]
3) -5 Log6
5 + a Log[2]
4) -Log6
5 - a Log[2]
5) Log216
125 - a Log[4]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=20 ⅇ-1+t millions of euros/year.
If the initial deposit in the investment fund was 60
millions of euros, compute the depositis available after 3 years.
1) 60 -20
ⅇ+ 20 ⅇ
2 millions of euros = 200.4235 millions of euros
2) 60 +20
ⅇ2-20
ⅇmillions of euros = 55.3491 millions of euros
3) 60 -20
ⅇ+ 20 ⅇ millions of euros = 107.008 millions of euros
4) 80 -20
ⅇmillions of euros = 72.6424 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(2 + 3 t)(cos(2πt)+2) euros.
Compute the average value of the shares along the first
3 months of the year (between t=0 and t=3).
1) -1
3euros = -0.3333 euros
2)20
3euros = 6.6667 euros
3) 13 euros
4)7
3euros = 2.3333 euros
35
Exercise 7Compute the area enclosed by the function f(x)=-24 + 8 x + 6 x2 - 2 x3
and the horizontal axis between the points x=-3 and x=3.
1)187
2= 93.5
2)189
2= 94.5
3) 39
4) 94
5) 92
6) 89
7) 95
8) 36
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(6 + 4 t))(cos(2πt)+1) per-unit.
The initial deposit in the account is 15 000 euros. Compute the deposit after 2 years.
1) 18351.0414 euros
2) 18321.0414 euros
3) 18331.0414 euros
4) 18341.0414 euros
36
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77024362
Exercise 1
Compute a
-2
(-1 + 2 a - 4 t + 8 a t - 12 t2 + 9 a t2 - 12 t3)ⅆt
1) -9 + 7 a
2) -11 (2 + a)
3) The rest of the solutions are not correct
4) 5 - 2 a
5) 9 + a
6) 3 + 8 a
Exercise 2
Compute 0
1
(-(-2 - t) Sin[t])ⅆt
1) -5.30887
2) -5.50544
3) -5.11154
4) -5.6845
5) 1.22056
6) -1.35076
Exercise 3
Compute -8
-5
(4
(-4 - t)2)ⅆt
1) -13.5317
2) -12.5635
3) -13.9718
4) 63.
5) 3.
6) -13.0486
37
Exercise 4
Compute 2
3 -4 - 4 t + a t
t + t2ⅆt
1) a Log4
3 - Log
81
16
2) -a Log16
9 + Log
9
4
3) -2 a Log4
3 + Log
3
2
4) -4 a Log4
3 - Log
3
2
5) -a Log4
3 - Log
9
4
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=1 + t + t3 + 3 t4 millions of euros/year.
If the initial deposit in the investment fund was 60
millions of euros, compute the depositis available after 2 years.
1)3752
5millions of euros = 750.4 millions of euros
2)1247
20millions of euros = 62.35 millions of euros
3)4671
20millions of euros = 233.55 millions of euros
4)436
5millions of euros = 87.2 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=sin(-2 + 9 t) euros.
Compute the average value of the shares along the first
2 π months of the year (between t=0 and t=2 π).
1) 0 euros
2) -90 euros
3) 50 euros
4) -10 euros
38
Exercise 7Compute the area enclosed by the function f(x)=
x + x2 and the horizontal axis between the points x=-2 and x=4.
1)97
3= 32.3333
2)85
3= 28.3333
3)197
6= 32.8333
4)100
3= 33.3333
5)203
6= 33.8333
6)191
6= 31.8333
7)91
3= 30.3333
8)86
3= 28.6667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
10sin(-7 + 8 t) per-unit.
The initial deposit in the account is 12 000 euros. Compute the deposit after 4 π years.
1) 11 910 euros
2) 12 010 euros
3) 12 000 euros
4) 11 930 euros
39
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77352873
Exercise 1
Compute -2 a
1
(4 - 12 a t - 9 t2 - 6 a t2 - 4 t3)ⅆt
1) The rest of the solutions are not correct
2) 0
3) 2 - 4 a
4) 11 - 3 a
5) 5 - 13 a
6) -6 - 12 a
Exercise 2
Compute 0
1
(ⅇ3+2 t
-12 t + 12 t2)ⅆt
1) -148.413
2) -120.513
3) -529.011
4) -296.826
5) -460.918
6) -564.481
Exercise 3
Compute -5
-2
(225
(2 + 5 t)2)ⅆt
1) -11 655.
2) -11.2137
3) -14.0306
4) -17.1831
5) -16.1033
6) 3.66848
40
Exercise 4
Compute 3
5 -4 + 2 t - 4 a t
-2 t + t2ⅆt
1) The rest of the solutions are not corret
2) -3 Log5
3 + a Log[3]
3) -4 ArcTanh[2] + 4 ArcTanh[4] - 4 a Log[3] + Log[9]
4) -5 Log5
3 - 4 a Log[3]
5) -4 Log5
3 + a Log[3]
6) a Log[3] - 2 Log[5] + Log[9]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(6 + 9 t)(cos(2πt)+2) millions of euros/year.
If the initial deposit in the investment fund was 30
millions of euros, compute the depositis available after 2 years.
1) 27 millions of euros
2) 90 millions of euros
3) 147 millions of euros
4) 51 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(5 + 4 t)(sin(2πt)+1) euros.
Compute the average value of the shares along the first
9 months of the year (between t=0 and t=9).
1)1
9-3 +
2
πeuros = -0.2626 euros
2)1
97 -
2
πeuros = 0.707 euros
3)1
9207 -
18
πeuros = 22.3634 euros
4)1
918 -
4
πeuros = 1.8585 euros
41
Exercise 7Compute the area enclosed by the function f(x)=-4 x + 2 x2
and the horizontal axis between the points x=-4 and x=-1.
1)153
2= 76.5
2)147
2= 73.5
3)151
2= 75.5
4) 75
5)149
2= 74.5
6) 76
7) 74
8) 72
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(6 + 9 t))(sin(2πt)+1) per-unit.
The initial deposit in the account is 16 000 euros. Compute the deposit after 2 years.
1) 21007.7898 euros
2) 21027.7898 euros
3) 20997.7898 euros
4) 20987.7898 euros
42
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77361996
Exercise 1
Compute 3 a
-3
(-6 - 3 a + 2 t + 30 a t - 15 t2 - 27 a t2 + 12 t3)ⅆt
1) The rest of the solutions are not correct
2) 405 (1 + a)
3) 5 - 3 a
4) -5 - 8 a
5) 7 - 11 a
6) -5 + 9 a
Exercise 2
Compute 0
1
(ⅇ-3+t
2 + t + 3 t2)ⅆt
1) 0.328167
2) -4.44251
3) 0.473673
4) 0.473673
5) -4.69068
6) -4.33436
Exercise 3
Compute -5
-2
(1
t4)ⅆt
1) -1.05574×106
2) 0.039
3) -4.33436
4) -4.44251
5) -4.69068
6) -2.93682
43
Exercise 4
Compute 4
5 -4 + 3 a + 4 t - a t
3 - 4 t + t2ⅆt
1) -a Log16
9 - 5 Log[2]
2) -a Log4
3 + Log[16]
3) a Log16
9 - Log[4]
4) 4 a Log4
3 + Log[8]
5) -a Log16
9 + Log[8]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=3 + t + 3 t4 millions of euros/year.
If the initial deposit in the investment fund was 80
millions of euros, compute the depositis available after 3 years.
1)3572
5millions of euros = 714.4 millions of euros
2)536
5millions of euros = 107.2 millions of euros
3)2393
10millions of euros = 239.3 millions of euros
4)841
10millions of euros = 84.1 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(-8 - 7 t)cos(9 t) euros.
Compute the average value of the shares along the first
π months of the year (between t=0 and t=π).
1) 0 euros
2)14
81 πeuros = 0.055 euros
3) 50 +14
81 πeuros = 50.055 euros
4)14
81 πeuros = 0.055 euros
44
Exercise 7Compute the area enclosed by the function f(x)=-9 + 9 x + x2 - x3
and the horizontal axis between the points x=-5 and x=3.
1)263
2= 131.5
2) 131
3) 130
4)261
2= 130.5
5)88
3= 29.3333
6)128
3= 42.6667
7) 128
8)344
3= 114.6667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(2 + 5 t))cos(t) per-unit.
The initial deposit in the account is 13 000 euros. Compute the deposit after 4 π years.
1) 12 990 euros
2) 12 980 euros
3) 13 000 euros
4) 13 050 euros
45
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77377313
Exercise 1
Compute a
-3
(2 - 5 a + 10 t - 20 a t + 30 t2 - 12 a t2 + 16 t3)ⅆt
1) 31 (3 + a)
2) 15 - 3 a
3) -13 - a
4) -11 - 5 a
5) 2 - 5 a
6) The rest of the solutions are not correct
Exercise 2
Compute -3
-2
(3 Cos[2 t])ⅆt
1) -1.01304
2) -4.49974
3) -4.02173
4) -3.39081
5) 0.71608
6) 12.5634
Exercise 3
Compute 5
7
(9
t5)ⅆt
1) -4.49974
2) -4.02173
3) 0.00266289
4) -3.39081
5) -3.36473
6) -25 506.
46
Exercise 4
Compute 1
2 -4 a + 4 t - 2 a t
2 t + t2ⅆt
1) -Log4
3 - a Log[4]
2) Log4
3 - a Log[2]
3) Log4
3 + a Log[4]
4) -Log4
3 - 5 a Log[2]
5) 4 Log4
3 + a Log[2]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=30 ⅇ3+2 t millions of euros/year.
If the initial deposit in the investment fund was 80
millions of euros, compute the depositis available after 2 years.
1) 80 + 15 ⅇ - 15 ⅇ3 millions of euros = -180.5088 millions of euros
2) 80 - 15 ⅇ3+ 15 ⅇ
7 millions of euros = 16228.2143 millions of euros
3) 80 - 15 ⅇ3+ 15 ⅇ
5 millions of euros = 2004.9143 millions of euros
4) 80 - 15 ⅇ3+ 15 ⅇ
9 millions of euros = 121324.9759 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(4 + 9 t)ⅇ-1+3 t euros.
Compute the average value of the shares along the first
4 months of the year (between t=0 and t=4).
1)1
4-
8
3 ⅇ4-
1
3 ⅇeuros = -0.0429 euros
2)1
4-
1
3 ⅇ+19 ⅇ5
3euros = 234.9568 euros
3)1
4-
1
3 ⅇ+10 ⅇ2
3euros = 6.1269 euros
4)1
4-
1
3 ⅇ+37 ⅇ11
3euros = 184611.9063 euros
47
Exercise 7Compute the area enclosed by the function f(x)=4 x + 2 x2
and the horizontal axis between the points x=-4 and x=-1.
1)115
6= 19.1667
2)50
3= 16.6667
3)103
6= 17.1667
4)44
3= 14.6667
5)56
3= 18.6667
6)53
3= 17.6667
7)109
6= 18.1667
8) 12
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
13(2 + 2 t))ⅇ-3+t per-unit.
The initial deposit in the account is 8000 euros. Compute the deposit after 1 year.
1) 8218.3126 euros
2) 8148.3126 euros
3) 8198.3126 euros
4) 8168.3126 euros
48
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77380424
Exercise 1
Compute -2 a
1
(6 + 2 a + 2 t + 8 a t + 6 t2 - 12 a t2 - 8 t3)ⅆt
1) -4 - 8 a
2) The rest of the solutions are not correct
3) 10 - 14 a
4) -1 - 14 a
5) 7 + 14 a
6) -4 - 13 a
Exercise 2
Compute -1
0
(ⅇ3-3 t
(6 - 9 t))ⅆt
1) -1412.
2) -6354.33
3) 1593.63
4) 4236.
5) -7115.37
6) -6624.55
Exercise 3
Compute 0
6
(-250
(-2 - 5 t)3)ⅆt
1) 6.22559
2) -27.7965
3) -16.3665
4) -24.8235
5) -524 280.
6) -25.8791
49
Exercise 4
Compute 2
3 -12 - 4 t - 4 a t
3 t + t2ⅆt
1) -2 a Log6
5 + Log
3
2
2) -4 a Log6
5 + Log
9
4
3) -a Log6
5 + Log
9
4
4) -4 a Log6
5 + Log
3
2
5) The rest of the solutions are not corret
6) 3 -a Log6
5 + Log
3
2
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(4 + 8 t)(cos(2πt)+2) millions of euros/year.
If the initial deposit in the investment fund was 20
millions of euros, compute the depositis available after 2 years.
1) 68 millions of euros
2) 20 millions of euros
3) 36 millions of euros
4) 116 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=3 t + t2 + t4 euros.
Compute the average value of the shares along the first
6 months of the year (between t=0 and t=6).
1)237
20euros = 11.85 euros
2)1401
5euros = 280.2 euros
3)61
180euros = 0.3389 euros
4)113
45euros = 2.5111 euros
50
Exercise 7Compute the area enclosed by the function f(x)=
-3 x - x2 and the horizontal axis between the points x=-5 and x=4.
1)99
2= 49.5
2)117
2= 58.5
3) 60
4)193
6= 32.1667
5)247
6= 41.1667
6)121
2= 60.5
7) 61
8)123
2= 61.5
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
1003 + t + 3 t3 per-unit.
The initial deposit in the account is 13 000 euros. Compute the deposit after 2 years.
1) 15968.2359 euros
2) 15878.2359 euros
3) 15868.2359 euros
4) 15858.2359 euros
51
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77383294
Exercise 1
Compute 3 a
2
(-3 + 30 a - 20 t - 18 a t + 9 t2 - 18 a t2 + 8 t3)ⅆt
1) 9 - 4 a
2) The rest of the solutions are not correct
3) 15 - 14 a
4) 10 - 15 a
5) 7 - a
6) 5 - 10 a
Exercise 2
Compute 1
3
(-(-6 + 6 t) Sin[3 - 2 t])ⅆt
1) -34.195
2) -29.8913
3) 3.64451
4) -30.8699
5) -1.25433
6) 7.41384
Exercise 3
Compute -4
-3
(9375
(-2 + 5 t)5)ⅆt
1) 2.23106×107
2) -4.16382
3) -4.02325
4) -0.00361134
5) -4.61232
6) -4.03182
52
Exercise 4
Compute 3
4 -2 + t + 5 a t
-2 t + t2ⅆt
1) -5 Log4
3 + a Log[16]
2) -2 ArcTanh[2] + 2 ArcTanh[3] + Log[2] + a Log[32]
3) -Log4
3 - a Log[8]
4) 4 Log4
3 + a Log[2]
5) The rest of the solutions are not corret
6) -2 Log[4] + a Log[8] + Log[9]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(1 + 4 t)log(4 t) millions of euros/year.
If, for t=1, the deposits in the investment fund were 70
millions euros, compute the deposit available after (with respect to t=1) 5 years.
1) 42 - 3 Log[4] + 55 Log[20] millions of euros = 202.6064 millions of euros
2) 60 - 3 Log[4] + 78 Log[24] millions of euros = 303.7293 millions of euros
3) 30 - 3 Log[4] + 78 Log[24] millions of euros = 273.7293 millions of euros
4) 52 - 3 Log[4] + 36 Log[16] millions of euros = 147.6543 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(3 + 6 t)(cos(2πt)+2) euros.
Compute the average value of the shares along the first
4 months of the year (between t=0 and t=4).
1) 9 euros
2) 30 euros
3) 0 euros
4) 3 euros
53
Exercise 7Compute the area enclosed by the function f(x)=-6 x + 5 x2 - x3
and the horizontal axis between the points x=-2 and x=5.
1)673
12= 56.0833
2)667
12= 55.5833
3)563
12= 46.9167
4)637
12= 53.0833
5)661
12= 55.0833
6)679
12= 56.5833
7)655
12= 54.5833
8)77
12= 6.4167
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(2 + 6 t))(cos(2πt)+1) per-unit.
The initial deposit in the account is 16 000 euros. Compute the deposit after 5 years.
1) 37494.3496 euros
2) 37484.3496 euros
3) 37434.3496 euros
4) 37474.3496 euros
54
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77386231
Exercise 1
Compute 2 a
3
(-15 - 2 a + 2 t - 68 a t + 51 t2 - 30 a t2 + 20 t3)ⅆt
1) The rest of the solutions are not correct
2) 13 - 11 a
3) 828 - 552 a
4) -1 - 15 a
5) -4 - 15 a
6) -10 - 14 a
Exercise 2
Compute -1
1
(-ⅇ-3+2 t
)ⅆt
1) -3.2407
2) -4.36867
3) -0.180571
4) -0.374617
5) -3.27999
6) -4.85238
Exercise 3
Compute 5
7
(14
-5 + 2 t)ⅆt
1) -19.9651
2) 0.587787
3) 4.11451
4) -13.4955
5) -13.3339
6) -17.9749
55
Exercise 4
Compute 3
4 -8 a + t + 4 a t
-2 t + t2ⅆt
1) 5 a Log4
3 - 4 Log[2]
2) a Log16
9 - 4 Log[2]
3) The rest of the solutions are not corret
4) -a Log16
9 - 5 Log[2]
5) 4 a Log4
3 + Log[2]
6) -3 a Log4
3 - 5 Log[2]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(8 + 7 t)(sin(2πt)+1) millions of euros/year.
If the initial deposit in the investment fund was 90
millions of euros, compute the depositis available after 4 years.
1) 178 -14
πmillions of euros = 173.5437 millions of euros
2) 120 -7
πmillions of euros = 117.7718 millions of euros
3)203
2-
7
2 πmillions of euros = 100.3859 millions of euros
4)171
2+
7
2 πmillions of euros = 86.6141 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(9 + 2 t)ⅇ1+2 t euros.
Compute the average value of the shares along the first
6 months of the year (between t=0 and t=6).
1)1
6-4 ⅇ + 10 ⅇ
13 euros = 737353.8412 euros
2)1
6
3
ⅇ- 4 ⅇ euros = -1.6282 euros
3)1
6-4 ⅇ + 5 ⅇ
3 euros = 14.9258 euros
4)1
6-4 ⅇ + 6 ⅇ
5 euros = 146.601 euros
56
Exercise 7Compute the area enclosed by the function f(x)=
-2 x + x2 and the horizontal axis between the points x=-4 and x=0.
1)127
3= 42.3333
2)121
3= 40.3333
3)245
6= 40.8333
4)251
6= 41.8333
5)112
3= 37.3333
6)239
6= 39.8333
7)233
6= 38.8333
8)124
3= 41.3333
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(-1 + t
97236)ⅇ
3+3 t per-unit.
The initial deposit in the account is 3000 euros. Compute the deposit after 2 years.
1) 3056.3543 euros
2) 3057.5886 euros
3) 3036.3543 euros
4) 3076.3543 euros
57
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77387031
Exercise 1
Compute -2 a
4
(-2 - 4 a - 4 t + 28 a t + 21 t2 - 18 a t2 - 12 t3)ⅆt
1) 3 + 2 a
2) The rest of the solutions are not correct
3) -7 - 5 a
4) -10 - 2 a
5) 15 - 13 a
6) 1 - 15 a
Exercise 2
Compute -5
-1
(-2 Log[-t])ⅆt
1) -34.3698
2) 32.4719
3) -37.5705
4) -16.0944
5) -8.09438
6) -39.7253
Exercise 3
Compute 2
6
(100
(-2 - 5 t)2)ⅆt
1) -4.83495
2) 1.04167
3) -4.00762
4) -4.42305
5) -5.11225
6) 31 040.
58
Exercise 4
Compute 0
2 -6 - 4 a - 2 t - 4 a t
3 + 4 t + t2ⅆt
1) The rest of the solutions are not corret
2) -5 a Log5
3 + Log[3]
3) 3 a Log5
3 - 3 Log[3]
4) -5 a Log5
3 + Log[3]
5) 3 a Log5
3 - 5 Log[3]
6) 4 a Log5
3 - 5 Log[3]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(3 + 2 t)(sin(2πt)+1) millions of euros/year.
If the initial deposit in the investment fund was 20
millions of euros, compute the depositis available after 2 years.
1) 30 -2
πmillions of euros = 29.3634 millions of euros
2) 18 +1
πmillions of euros = 18.3183 millions of euros
3) 24 -1
πmillions of euros = 23.6817 millions of euros
4) 38 -3
πmillions of euros = 37.0451 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=t2 + 2 t3 + t4 euros.
Compute the average value of the shares along the first
9 months of the year (between t=0 and t=9).
1)256
135euros = 1.8963 euros
2)109
10euros = 10.9 euros
3)31
270euros = 0.1148 euros
4)17 037
10euros = 1703.7 euros
59
Exercise 7Compute the area enclosed by the function f(x)=9 x + 12 x2 + 3 x3
and the horizontal axis between the points x=-5 and x=5.
1) 1000
2)2363
2= 1181.5
3) 1182
4) 1181
5)2357
2= 1178.5
6) 1180
7) 1176
8) 1160
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
1003 t2 + 2 t3 per-unit.
The initial deposit in the account is 12 000 euros. Compute the deposit after 2 years.
1) 14122.1305 euros
2) 14102.1305 euros
3) 14082.1305 euros
4) 14062.1305 euros
60
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77434209
Exercise 1
Compute -2 a
2
(9 + 56 a t + 42 t2 - 30 a t2 - 20 t3)ⅆt
1) The rest of the solutions are not correct
2) -4 - 9 a
3) -9 - 7 a
4) 7 - 9 a
5) 8 - 8 a
6) -1 - 14 a
Exercise 2
Compute -2
-1
(12 + 8 t - 12 t2 Log[-2 t])ⅆt
1) -119.768
2) 17.3147
3) -142.907
4) -149.268
5) -32.7103
6) -36.0437
Exercise 3
Compute 4
8
(-6250
(2 - 5 t)5)ⅆt
1) -7.44231×108
2) -3.39153
3) -3.66147
4) -4.36886
5) 0.002827
6) -4.56334
61
Exercise 4
Compute 5
7 15 - 9 a - 5 t - 3 a t
-9 + t2ⅆt
1) -4 Log5
4 + a Log[8]
2) -3 Log5
4 + a Log[8]
3) -5 Log5
4 + a Log[2]
4) -Log25
16 - a Log[2]
5) The rest of the solutions are not corret
6) -5 Log5
4 - a Log[8]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(6 + t)ⅇ-2+t millions of euros/year.
If the initial deposit in the investment fund was 20
millions of euros, compute the depositis available after 2 years.
1) 27 -5
ⅇ2millions of euros = 26.3233 millions of euros
2) 20 -5
ⅇ2+ 8 ⅇ millions of euros = 41.0696 millions of euros
3) 20 -5
ⅇ2+6
ⅇmillions of euros = 21.5306 millions of euros
4) 20 +4
ⅇ3-
5
ⅇ2millions of euros = 19.5225 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(4 + 3 t + 4 t2)log(5 t) euros.
Compute the average value of shares between month 1 and month 2 (between t=1 and t=2).
1)1
2-230
9-41 Log[5]
6+123 Log[15]
2euros = 64.9959 euros
2) -230
9-41 Log[5]
6+123 Log[15]
2euros = 129.9917 euros
3)1
2-205
4-41 Log[5]
6+376 Log[20]
3euros = 156.6086 euros
4) -337
36-41 Log[5]
6+74 Log[10]
3euros = 36.4382 euros
62
Exercise 7Compute the area enclosed by the function f(x)=
27 - 3 x2 and the horizontal axis between the points x=-1 and x=2.
1) 74
2) 77
3)151
2= 75.5
4) 72
5)149
2= 74.5
6) 75
7)153
2= 76.5
8) 76
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
1002 + 4 t + t2)log(2 t) per-unit.
In the year t=1 we deposint in the account 3000
euros. Compute the deposit in the account after (with respect to t=1) 3 years.
1) 7867.1544 euros
2) 7907.1544 euros
3) 7857.1544 euros
4) 7877.1544 euros
63
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77644810
Exercise 1
Compute -3 a
0
(-5 - 30 a - 20 t - 24 a t - 12 t2 + 9 a t2 + 4 t3)ⅆt
1) 3 - 2 a
2) 9 - 10 a
3) -2 - 8 a
4) -15 a
5) The rest of the solutions are not correct
6) 7 - 15 a
Exercise 2
Compute -3
1
((-3 - 2 t) Sin[2 + t])ⅆt
1) -5.29424
2) -24.7166
3) -0.56448
4) -3.95997
5) -25.2937
6) -23.1608
Exercise 3
Compute 2
4
(12
-3 + 3 t)ⅆt
1) -20.5159
2) 4.39445
3) -17.8923
4) -20.9949
5) -19.2245
6) 1.09861
64
Exercise 4
Compute 2
3 3 - 10 a - 3 t - 5 a t
-2 + t + t2ⅆt
1) Log5
4 + a Log[2]
2) Log125
64 - a Log[2]
3) -5 a Log[2] - 3 Log[5] + Log[64]
4) 3 Log5
4 - a Log[2]
5) -Log5
4 + a Log[2]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(2 + 3 t)log(t) millions of euros/year.
If, for t=1, the deposits in the investment fund were 80
millions euros, compute the deposit available after (with respect to t=1) 4 years.
1)251
4+ 32 Log[4] millions of euros = 107.1114 millions of euros
2) 54 +95 Log[5]
2millions of euros = 130.4483 millions of euros
3)175
4+ 66 Log[6] millions of euros = 162.0061 millions of euros
4) 94 +95 Log[5]
2millions of euros = 170.4483 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(6 - t)cos(t) euros.
Compute the average value of the shares along the first
π months of the year (between t=0 and t=π).
1) 30 +2
πeuros = 30.6366 euros
2) 40 +2
πeuros = 40.6366 euros
3) 0 euros
4)2
πeuros = 0.6366 euros
65
Exercise 7Compute the area enclosed by the function f(x)=6 - x - 4 x2 - x3
and the horizontal axis between the points x=-4 and x=0.
1)71
6= 11.8333
2)89
6= 14.8333
3)43
3= 14.3333
4)83
6= 13.8333
5)40
3= 13.3333
6) 4
7)32
3= 10.6667
8)17
6= 2.8333
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(8 - 9 t))cos(t) per-unit.
The initial deposit in the account is 7000 euros. Compute the deposit after 2 π years.
1) 7060 euros
2) 7040 euros
3) 7000 euros
4) 6970 euros
66
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77646467
Exercise 1
Compute -2 a
3
(-12 + 14 a + 14 t - 64 a t - 48 t2 + 30 a t2 + 20 t3)ⅆt
1) 13 - 12 a
2) 1 - 9 a
3) -2 - 14 a
4) -8 + 7 a
5) 0
6) The rest of the solutions are not correct
Exercise 2
Compute -3
-2
((2 + 2 t) Log[-t])ⅆt
1) 0.887511
2) -10.4026
3) -7.79367
4) -2.79584
5) -7.59245
6) -9.7109
Exercise 3
Compute 1
7
(45
(-4 - 3 t)2)ⅆt
1) -5.74056
2) -5.35887
3) -4.18982
4) 1.54286
5) 15 282.
6) -4.30087
67
Exercise 4
Compute 2
3 4 - 2 a + 2 t - 2 a t
2 + 3 t + t2ⅆt
1) -4 a Log5
4 - 5 Log
4
3
2) The rest of the solutions are not corret
3) 2 a Log5
4 - Log
4
3
4) 4 a Log5
4 - 5 Log
4
3
5) -2 a Log5
4 + Log
16
9
6) -a Log5
4 + Log
4
3
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=30 ⅇ-3+3 t millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 3 years.
1) 40 -10
ⅇ3+ 10 ⅇ
3 millions of euros = 240.3575 millions of euros
2) 50 -10
ⅇ3millions of euros = 49.5021 millions of euros
3) 40 +10
ⅇ6-10
ⅇ3millions of euros = 39.5269 millions of euros
4) 40 -10
ⅇ3+ 10 ⅇ
6 millions of euros = 4073.7901 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=10 ⅇ-2+t euros.
Compute the average value of the shares along the first
9 months of the year (between t=0 and t=9).
1)1
9-10
ⅇ2+10
ⅇeuros = 0.2584 euros
2)1
910 -
10
ⅇ2euros = 0.9607 euros
3)1
9-10
ⅇ2+ 10 ⅇ
7 euros = 1218.3309 euros
4)1
9
10
ⅇ3-10
ⅇ2euros = -0.0951 euros
68
Exercise 7Compute the area enclosed by the function f(x)=-18 - 33 x - 18 x2 - 3 x3
and the horizontal axis between the points x=2 and x=5.
1)6257
4= 1564.25
2)6251
4= 1562.75
3)6245
4= 1561.25
4)6249
4= 1562.25
5)6243
4= 1560.75
6)6255
4= 1563.75
7)6237
4= 1559.25
8)6253
4= 1563.25
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
9ⅇ-6+3 t per-unit.
The initial deposit in the account is 12 000 euros. Compute the deposit after 2 years.
1) 12511.6343 euros
2) 12471.6343 euros
3) 12451.6343 euros
4) 12491.6343 euros
69
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77688139
Exercise 1
Compute -2 a
1
(-5 - 8 a - 8 t + 24 a t + 18 t2 + 30 a t2 + 20 t3)ⅆt
1) -13 - 15 a
2) 13 - 14 a
3) -4 - 15 a
4) 1 - 15 a
5) The rest of the solutions are not correct
6) 12 - 10 a
Exercise 2
Compute -5
-3
(-3 - t2 Log[-t])ⅆt
1) -54.5376
2) -243.08
3) 167.349
4) -223.666
5) -194.504
6) -71.4265
Exercise 3
Compute 4
7
(40
-3 + 5 t)ⅆt
1) -13.6957
2) -18.0468
3) 5.06018
4) -22.5538
5) 0.632523
6) -20.7525
70
Exercise 4
Compute 4
5 9 - 3 t - 3 a t
-3 t + t2ⅆt
1) -Log5
4 - 5 a Log[2]
2) The rest of the solutions are not corret
3) -4 Log5
4 - a Log[4]
4) Log25
16 + a Log[2]
5) 5 Log5
4 - a Log[2]
6) 4 Log5
4 - a Log[2]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(1 + 5 t)ⅇ3+3 t millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 1 year.
1) 40 +2 ⅇ3
9+13 ⅇ6
9millions of euros = 627.1939 millions of euros
2) 40 +2 ⅇ3
9+43 ⅇ12
9millions of euros = 777650.6891 millions of euros
3)343
9+2 ⅇ3
9millions of euros = 42.5746 millions of euros
4) 40 +2 ⅇ3
9+28 ⅇ9
9millions of euros = 25254.0579 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(1 + t)log(3 t) euros.
Compute the average value of shares between month 1 and month 2 (between t=1 and t=2).
1)1
2-4 -
3 Log[3]
2+15 Log[9]
2euros = 5.4156 euros
2) -7
4-3 Log[3]
2+ 4 Log[6] euros = 3.7691 euros
3) -4 -3 Log[3]
2+15 Log[9]
2euros = 10.8313 euros
4)1
2-27
4-3 Log[3]
2+ 12 Log[12] euros = 10.7105 euros
71
Exercise 7Compute the area enclosed by the function f(x)=
-9 x + 3 x2 and the horizontal axis between the points x=-5 and x=5.
1) 277
2) 250
3) 279
4) 198
5)559
2= 279.5
6) 225
7)557
2= 278.5
8) 280
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(1 + 2 t))log(t) per-unit.
In the year t=1 we deposint in the account 15 000
euros. Compute the deposit in the account after (with respect to t=1) 3 years.
1) 17909.7799 euros
2) 17839.7799 euros
3) 17799.7799 euros
4) 17819.7799 euros
72
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77770524
Exercise 1
Compute -2 a
-2
(-4 + 14 a + 14 t - 28 a t - 21 t2 + 24 a t2 + 16 t3)ⅆt
1) 3 - 8 a
2) -156 (-1 + a)
3) The rest of the solutions are not correct
4) 15 - 13 a
5) 1 - 9 a
6) 3 - 12 a
Exercise 2
Compute -5
-4
(Log[-2 t])ⅆt
1) -6.52965
2) -9.65332
3) -15.2936
4) -6.73112
5) -10.7439
6) 2.19516
Exercise 3
Compute -7
-2
(567
(4 - 3 t)4)ⅆt
1) 0.058968
2) -2.97457
3) 3.22188×106
4) -3.06635
5) -4.39755
6) -4.89436
73
Exercise 4
Compute 2
5 -8 + 3 a - 4 t - 3 a t
-2 + t + t2ⅆt
1) -3 a Log7
4 - 4 Log[4]
2) The rest of the solutions are not corret
3) -5 a Log7
4 + Log[4]
4) 2 -2 a Log7
4 + Log[4]
5) -2 a Log7
4 + Log[4]
6) 4 a Log7
4 - Log[4]
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(4 + 2 t)ⅇ-3+2 t millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 2 years.
1) 40 +1
2 ⅇ5-
3
2 ⅇ3millions of euros = 39.9287 millions of euros
2) 40 -3
2 ⅇ3+
5
2 ⅇmillions of euros = 40.845 millions of euros
3) 40 -3
2 ⅇ3+7 ⅇ
2millions of euros = 49.4393 millions of euros
4) 40 -3
2 ⅇ3+9 ⅇ3
2millions of euros = 130.3102 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=20 ⅇ1+t euros.
Compute the average value of the shares along the first
5 months of the year (between t=0 and t=5).
1)1
5-20 ⅇ + 20 ⅇ
6 euros = 1602.842 euros
2)1
5-20 ⅇ + 20 ⅇ
2 euros = 18.6831 euros
3)1
5(20 - 20 ⅇ) euros = -6.8731 euros
4)1
5-20 ⅇ + 20 ⅇ
3 euros = 69.469 euros
74
Exercise 7Compute the area enclosed by the function f(x)=
6 - 3 x - 3 x2 and the horizontal axis between the points x=-4 and x=3.
1)77
2= 38.5
2)131
2= 65.5
3) 69
4)137
2= 68.5
5)27
2= 13.5
6) 68
7)135
2= 67.5
8) 67
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=1
15ⅇ-4+2 t per-unit.
The initial deposit in the account is 7000 euros. Compute the deposit after 2 years.
1) 7222.8486 euros
2) 7232.8486 euros
3) 7302.8486 euros
4) 7292.8486 euros
75
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 77771717
Exercise 1
Compute -3 a
-1
(2 + 33 a + 22 t + 90 a t + 45 t2 + 45 a t2 + 20 t3)ⅆt
1) The rest of the solutions are not correct
2) -1 + 3 a
3) -9 - 11 a
4) 14 - 13 a
5) -12 - 7 a
6) 5 - 6 a
Exercise 2
Compute 0
2
(-3 Sin[1 + 2 t])ⅆt
1) -4.12406
2) 5.75355
3) -3.97788
4) -3.75701
5) 0.850987
6) -0.38496
Exercise 3
Compute 1
9
(30
-3 + 5 t)ⅆt
1) -60.4915
2) -68.6297
3) -75.3348
4) 3.04452
5) 18.2671
6) -72.6644
76
Exercise 4
Compute 3
4 -10 + 15 a + 5 t + 5 a t
-6 + t + t2ⅆt
1) Log343
216 - a Log[2]
2) 5 Log7
6 + a Log[2]
3) Log49
36 - a Log[4]
4) Log343
216 - a Log[4]
5) -Log7
6 - a Log[2]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=(4 + 2 t)log(2 t) millions of euros/year.
If, for t=1, the deposits in the investment fund were 40
millions euros, compute the deposit available after (with respect to t=1) 4 years.
1)41
2- 5 Log[2] + 32 Log[8] millions of euros = 83.5764 millions of euros
2)5
2- 5 Log[2] + 60 Log[12] millions of euros = 148.1287 millions of euros
3) 32 - 5 Log[2] + 45 Log[10] millions of euros = 132.1506 millions of euros
4) 12 - 5 Log[2] + 45 Log[10] millions of euros = 112.1506 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(6 + 8 t)(cos(2πt)+1) euros.
Compute the average value of the shares along the first
8 months of the year (between t=0 and t=8).
1)5
4euros = 1.25 euros
2) -1
4euros = -0.25 euros
3) 38 euros
4)7
2euros = 3.5 euros
77
Exercise 7Compute the area enclosed by the function f(x)=
-6 x + x2 + x3 and the horizontal axis between the points x=-3 and x=3.
1)27
2= 13.5
2) 18
3)86
3= 28.6667
4)187
6= 31.1667
5)95
3= 31.6667
6)92
3= 30.6667
7)193
6= 32.1667
8)181
6= 30.1667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(9 + 2 t))(cos(2πt)+1) per-unit.
The initial deposit in the account is 3000 euros. Compute the deposit after 3 years.
1) 4329.9882 euros
2) 4299.9882 euros
3) 4349.9882 euros
4) 4319.9882 euros
78
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 78028660
Exercise 1
Compute -a
5
(6 + 5 a + 10 t + 26 a t + 39 t2 + 12 a t2 + 16 t3)ⅆt
1) The rest of the solutions are not correct
2) -11 - 12 a
3) -1 - 6 a
4) 856 (5 + a)
5) 11 - 13 a
6) -9 - 7 a
Exercise 2
Compute -1
3
(-Cos[2 + t])ⅆt
1) 1.8004
2) -1.39129
3) -7.84383
4) -8.53449
5) -7.30382
6) -6.42776
Exercise 3
Compute -7
0
(54
(1 - 3 t)2)ⅆt
1) -69.7029
2) -74.8565
3) 17.1818
4) -61.3425
5) -81.4477
6) 10 647.
79
Exercise 4
Compute 3
4 -2 a - 3 t + 2 a t
-t + t2ⅆt
1) The rest of the solutions are not corret
2) 5 -a Log4
3 + Log
3
2
3) -5 a Log4
3 + Log
3
2
4) Log3
2 - a Log
64
27
5) -Log3
2 + a Log
16
9
6) Log3
2 + a Log
16
9
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=30 ⅇ2 t millions of euros/year.
If the initial deposit in the investment fund was 40
millions of euros, compute the depositis available after 3 years.
1) 25 + 15 ⅇ6 millions of euros = 6076.4319 millions of euros
2) 25 + 15 ⅇ2 millions of euros = 135.8358 millions of euros
3) 25 + 15 ⅇ4 millions of euros = 843.9723 millions of euros
4) 25 +15
ⅇ2millions of euros = 27.03 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(8 + 3 t)ⅇ-1+t euros.
Compute the average value of the shares along the first
4 months of the year (between t=0 and t=4).
1)1
4-5
ⅇ+ 17 ⅇ
3 euros = 84.9037 euros
2)1
4-5
ⅇ+ 11 ⅇ euros = 7.0154 euros
3)1
4
2
ⅇ2-5
ⅇeuros = -0.3922 euros
4)1
48 -
5
ⅇeuros = 1.5402 euros
80
Exercise 7Compute the area enclosed by the function f(x)=2 x - 2 x2
and the horizontal axis between the points x=-5 and x=-1.
1)661
6= 110.1667
2)649
6= 108.1667
3)326
3= 108.6667
4)329
3= 109.6667
5)335
3= 111.6667
6)332
3= 110.6667
7)667
6= 111.1667
8)320
3= 106.6667
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
560(-3 + t))ⅇ2+t per-unit.
The initial deposit in the account is 18 000 euros. Compute the deposit after 1 year.
1) 17089.7635 euros
2) 17039.7635 euros
3) 17064.3311 euros
4) 17059.7635 euros
81
Mathematics 1 - ADE/FyCo - 2019/2020List of exercises 03-Integration for identity number: 300530374
Exercise 1
Compute -3 a
-3
(9 a + 6 t + 84 a t + 42 t2 - 45 a t2 - 20 t3)ⅆt
1) -12 - 6 a
2) 9 - 4 a
3) The rest of the solutions are not correct
4) 756 (-1 + a)
5) -5 - 12 a
6) 10 - 9 a
Exercise 2
Compute 0
1
(ⅇ-3+2 t
12 - 8 t + 4 t2)ⅆt
1) 1.39131
2) -2.75881
3) -4.40982
4) -2.02317
5) 3.43354
6) -2.63266
Exercise 3
Compute 7
9
(1
t3)ⅆt
1) -1.3×106
2) 0.00403124
3) -3.16954
4) -1.89221
5) -1.98288
6) -1.45414
82
Exercise 4
Compute 4
6 6 + a - 3 t - a t
2 - 3 t + t2ⅆt
1) -4 Log5
3 + a Log[2]
2) Log5
3 - a Log[2]
3) -a Log[2] - 3 Log[5] + Log[27]
4) Log5
3 - 5 a Log[2]
5) -Log5
3 + a Log[4]
6) The rest of the solutions are not corret
Exercise 5The deposits of an investment fund vary from one year to
another being the speed of that variation determined by the function
v(t)=1 + 2 t2 + 2 t3 + 2 t4 millions of euros/year.
If the initial deposit in the investment fund was 20
millions of euros, compute the depositis available after 3 years.
1)9064
15millions of euros = 604.2667 millions of euros
2)677
30millions of euros = 22.5667 millions of euros
3)722
15millions of euros = 48.1333 millions of euros
4)1787
10millions of euros = 178.7 millions of euros
Exercise 6The true value of certain shares oscillates along the year.
The following function yields the value of the shares for each month t:
V(t)=(5 + 6 t)(cos(2πt)+1) euros.
Compute the average value of the shares along the first
4 months of the year (between t=0 and t=4).
1) 17 euros
2)11
2euros = 5.5 euros
3) -1
2euros = -0.5 euros
4) 2 euros
83
Exercise 7Compute the area enclosed by the function f(x)=
6 - 7 x + x3 and the horizontal axis between the points x=-2 and x=4.
1) 58
2)115
2= 57.5
3)111
2= 55.5
4)9
2= 4.5
5)117
2= 58.5
6) 54
7) 59
8) 57
Exercise 8Certain bank account offers a variable continuous compound
interes rate. The interest rate for each year is given by the function
I(t)=(1
100(3 + 7 t))(cos(2πt)+1) per-unit.
The initial deposit in the account is 17 000 euros. Compute the deposit after 3 years.
1) 25528.1425 euros
2) 25518.1425 euros
3) 25488.1425 euros
4) 25538.1425 euros
84