ab calc sect 5.3-notes ab calc assignment...
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AB Calc Assignment Page
Today's Topics & Class Plan:
Check Worksheet 5.2C
New Notes on Section 5.3
Return Derivatives Quiz
Assignments & Opportunities:Friday: Do p363; 3 - 15 odd
Monday: Kairos guys meet with Ms. H in room 109 at 2:30pm
AB Calc Sect 5.3-Notes
Thursday, December 15, 2011
Chapter 5 Page 1
AB Calculus - Hardtke Assignment 5.2C Name ________________________________
_______________________________ Write the simplest answer for each.
1.
11 13
3 11f (x)dx f (x)dx
2.
11 8
3 11f (x)dx f (x)dx
=
3. Given
11 3
3 11f (x)dx w, find f (x)dx
4.
8
8f (x)dx
5.
11
35dx = 6.
3
115dx = 7.
11
35 dx = 8.
3
115 dx =
9. Simplify each statement given q
pf (x)dx = n and r is an element of [p, q]:
a. r q
p rf (x)dx f (x)dx = b.
q r
p qf (x)dx f (x)dx =
c. q
p7f (x)dx = d.
p
pf (x)dx =
10. Given the shaded area below is m units2, 11. For f(x) shown below, estimate a
af (x)dx
=
finda
af (x)dx
12. Evaluate each definite integral using its graph: (Think visually. No need to use definition as infinite Riemann Sum)
A.
2
2
cos x dx
= B.
2
2x dx
= C.
0
5
3x dx
=
D.
5
53x dx
= E.
3
0x dx
= F.
6
0
x 2dx
x 2
=
- a a
- a
4
3.5
3
2.5
2
1.5
1
0.5
-2 -1 1 2
a
Chapter 5 Page 2
12. (Continued.) Evaluate each definite integral using its graph: (Think visually. No need to use definition as infinite
Riemann Sum)
G.
5
2(3x 1) dx
= H.
2
5(3x 1) dx
= I.
193
19x dx
=
J.
5
2(3x 1) dx
= K.
8
1x 2 dx
= L.
32
09 x dx
=
13. What is another way of writing n
i in
i 1
lim f (x ) x
over [a, b]? ______________________________________
14. Given11
3( ) 24f x dx
, what do you think is the average height of f(x) on this interval?__________
15. A. Use your calculator to find the Midpoint Riemann Sum using 4 equal partitions to approximate
9
12 3x dx
. __________
Show what you need to calculate in one line here:
B. Now use your calculator to find the Left Endpoint Riemann Sum using 4 equal intervals. ______________
Show what you need to calculate in one line here:
16. A. For an increasing function, Rn will produce a __________-estimate of the actual area.
B. For an decreasing function, Ln will produce a __________-estimate of the actual area.
By Definition of an Integral you must find the area under a curve by simplifying an infinite Riemann Sum.
Let's practice that by finding
Chapter 5 Page 3
Let's practice that by finding
Want to learn the shortcut?
By The Evaluation Theorem - Part 1 of The Fundamental Theorem of Calculus (FTC1)
The Evaluation Theorem - Part 1 of The Fundamental Theorem of Calculus (FTC1):
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Chapter 5 Page 7