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Test 3 for Math 132: Integrals Evaluation and Convergence - Prof. Cathy W. Carter, Exams of Calculus

A test for math 132 students, focusing on evaluating integrals and determining their convergence. The test includes 11 problems, some of which require calculator-free work. Students are allowed to omit one problem and receive full credit for the remaining ones. If they complete all problems, they will earn a bonus. The problems involve evaluating integrals using basic functions and setting up partial fraction decompositions.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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koofers-user-uzl 🇺🇸

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Math 132 Test 3 Carter Name______________________
Show all work in order to receive credit. Calculator-free 3/19/08
You may omit one problem – in which case each problem is worth 10 points. If you work all 11 problems, each
is worth 9 points & you will have a 5 point bonus.
1-7. Evaluate the integrals.
1.
3 2
cos 5 sin 5x x dx
2.
4 1
5 3
xdx
x x
3.
2
16 x dx
4.
2
24
xdx
x
5.
3
2
4
2 1
x x dx
x x
6.
2
2 6
1
xdx
x x
7.
2
tan sec secx x x dx
8. Set up the form for the partial fraction decomposition. You do not need to find the constants.
3
3 2 2
4 2 7
( 4)( 2 1)
x x
x x x x
9-11. Determine whether the following integrals converge or diverge. If an integral converges, find its value.
9.
10.
4
2
0( 1)
dx
x
11.
0
x
xe dx

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Download Test 3 for Math 132: Integrals Evaluation and Convergence - Prof. Cathy W. Carter and more Exams Calculus in PDF only on Docsity!

Math 132 Test 3 Carter Name______________________ Show all work in order to receive credit. Calculator-free 3/19/ You may omit one problem – in which case each problem is worth 10 points. If you work all 11 problems, each is worth 9 points & you will have a 5 point bonus. 1-7. Evaluate the integrals.

cos^3 5 x sin 2 5 x dx

x dx x x

3.  16  x dx^2

2 (^2 ) x dx

 x 

3 2

x x dx x x

2

x dx x x

2

^ tan^ x^ sec^ x^ sec x^ dx

  1. Set up the form for the partial fraction decomposition. You do not need to find the constants. 3 3 2 2

x x x x x x

9-11. Determine whether the following integrals converge or diverge. If an integral converges, find its value.

4 0 x dx

4 2 0 (^ 1) dx

 x 

0 xe xdx  