CLASS IDS: SURNAMES: SCORE:

M5 4PS SY1112 ANSWER SHEET

FILL IN THE BLANKS (10 points)

1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

MULTIPLE CHOICE (20 points)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 1 2. 13. 14. 15. 16. 17. 18. 19. 20.

DLMGUTIERREZ

FITB: Fill in the blanks with the most appropriate response.

1. If 4

2f x dx 3

then

2 41 3

4 1 3 4

f dx f dx f dx f dxx x x x

2. 2 4

4 2

2 2tan x secdx x dx

= ___.

3. Let

1

1

g(x)dx 4

and

1

0

f(x)dx 5 . If g(x) is even and f(x) is odd then

0

1

g(x) f(x) dx

= ___.

4. The area of the region bounded by the curve 2 216x 25y 400 0 is __.

5. Suppose 3

6

bx x2 2

a

csc cot dx 2 cscucotudu

. Then the value of (b – a) is ___.

6. If

0

cos2x dx 0

then 2

0

sin x dx

= ___.

7.

4

3

x

x

x

dtD

t = ___.

8. x 2cot x

dtD

1 t

= ___.

9. The positive number b that will maximize the value of the integral b

2

4 x dx

is ___.

10. The maximum value of the integral b

2

4 x dx

is ___.

MC: Write the letter of the best answer.

1. What polygon is formed by the region represented by the integral 1

4

3 x 1 dx

?

A. kite B. pentagon C. trapezoid D. trapezium

2. What is the area of the region indicated in #1?

A. 7.5 B. 8 C. 8.5 D. 9

3. Which integral DOES NOT give the area of the region bounded by sin x, the lines y = 0,

x = 0 and x = 2?

A. 2

0

sin xdx

C.

2

0

sinxdx sinxdx

B.

2

4 sin xdx

D.

0 2

sinxdx sinxdx

4. What is the area of the region indicated in #3?

A. 0 B. 1 C. 2 D. 4

5. Which integral represents the area of the shaded region?

A. 2

1

2x 1 dx

B. 0.5 2

1 0.5

2x 1 dx 2x 1 dx

C. 2 1

0.5 0.5

2x 1 dx 2x 1 dx

D. 0.5 2

1 0.5

1 2x dx 2x 1 dx

6. What is the area of the region indicated in #5?

A. 3 B. 4.5 C. 6 D. 9

7. Graph the integrand and use geometry to evaluate the integral 3

3

x 10 dx

A. 69 B. 129 C. 78 D. 39

8. Graph the integrand and use geometry to evaluate the integral 6

2

6

36 x dx

A. 36 B. 36 C. 18 D. 6

9. Which integral represents the area bounded by the curve 3

y x 2 , the x-axis

and the line x 1 and x 3 ?

A. 3

3

1

x 2 dx C.

3 23 3

2 1

x 2 dx x 2 dx

B. 3

3

1

x 2 dx D.

3

3

2 23 3

1 2

x 2 dx x 2 dx

10. What is the area bounded by the curve 3

y x 2 , the x-axis and the line

x 1 and x 3 ?

A. 0 B. 14

C. 12

D. 1

11. Which theorem states that “ If a function F is continuous on the closed interval [a, b]

and F’(x) = f(x) for all x in [a, b] then

b

a

f(t)dt F(b) F(a)

A. MVT B. FTC1 C. FTC2 D. EVT

x

y

F(x)

12. Let b 1

2af x dx ;

b 52a

g x dx ; b 7

6af x g x dx ;

b 2 1

3af x dx ; and

b 2 193a

g x dx . Evaluate 2b

af x g x dx .

A. 133

B. 203

C. 256

D. 4

13. Find the average value of 2y x 2x 6 on the closed interval [0, 2].

A. 6 B. 163

C. 343

D. 5

14. Find the average value of the sine function on the closed interval [– , 0].

A. 1

B. 2

C.

2

D. 0

15. Find the value of x at which the average value of the function defined by

2f x 4 x occurs on the interval [0, 2]

A. 2 2

3 B.

2 3

3 C.

2 D. 8

3

16. Evaluate the integral

1 4 2

21

x 2x 1dx

x 1

.

A. 4

3

B.

2

3

C.

1

3 D.

4

3

17. Evaluate the integral

0

9 sin4xdx.

4

A. 9

4

B.

9

4

C.

9 1

4 8

D.

9 1

4 8

18. Suppose 8

7

f x dx 2 . Find 8

7

5f x dx and 7

8

f x dx .

A. –10; –1/2 B. –10; 2 C. 3; –2 D. 5; 2

19. Suppose that f is continuous and that 3

3

f x dx 0

and 6

3

f x dx 3

. Find

6

3

Find 4f x dx.

A. – 3 B. – 4 C. 12 D. – 12

20. Find the derivative of

x

0

y 6t 5 dt.

A. 6x 5 B. 6x 5 5 C. 6x 5

3

D. 3/21

6x 59

END OF PROBLEM SET