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8.3 Trigonometric Integrals
494
c.
d.
e.
____ 14. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 15. Find the indefinite integral.
a.
b.
c.
d.
e.
495 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 16. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 17. Solve.
a.
b.
c.
d.
e.
____ 18. Find .
a.
b.
c.
d.
e.
8.3 Trigonometric Integrals
496
____ 19. Find .
a.
b.
c.
d.
e.
____ 20. Evaluate .
a.
b.
c.
d.
e.
497 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.3 Trigonometric Integrals
Answer Section
8.4 Trigonometric Substitution
498
8.4 Trigonometric Substitution
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
499 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 3. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 4. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution
500
____ 5.
Find the indefinite integral by making the substitution
.
a.
b.
c.
d.
e.
____ 6. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
501
Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____
7.
Find the indefinite integral by making the substitution
.
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution
502
____ 9. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 10. Find .
a.
b.
c.
d.
e.
503
Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____
11.
Find the indefinite integral.
a.
b.
c.
d.
e.
____ 12. Find the indefinite integral.
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution
504
____ 13.
Find
.
a.
b.
c.
d.
e.
____ 14. Complete the square and find .
a.
b.
c.
d.
e.
505 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 15. Evaluate the integral using the integration limits. Round your answer
to three decimal places.
a.
b.
c.
d.
e.
____ 16. Find the definite integral.
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution
506
8.4 Trigonometric Substitution
Answer Section
507 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.5 Partial Functions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
____ 2. Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
8.5 Partial Functions
508
____ 3.
Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
____ 4. Use partial fractions to find .
a.
b.
c.
d.
e.
509 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 5. Use partial fractions to find the integral .
a.
b.
c.
d.
e.
____ 6. Use partial fractions to find the integral .
a.
b.
c.
d.
e.
____ 7. Use partial fractions to find
a.
b.
c.
8.5 Partial Functions
510
d.
e.
____ 8. Use partial fractions to find the integral
a.
b.
c.
d.
e.
____ 9.
Use partial fractions to find
.
a.
(1/ 5 )arctan(x/
5 )
b.
c.
(1/ 5 )arcsin(x/ 5 )+C
d.
e.
arctan(x/ 10 )
511 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 10. Evaluate the definite integral .
a.
b.
c.
d.
e.
____ 11. Use substitution to find the integral .
a.
b.
c.
8.5 Partial Functions
512
d.
e.
____ 12. The predicted cost C (in hundreds of thousands of dollars) for a company to remove p% of
a chemical from its waste water is shown in the table below. A model for the data is given by
. Use the model to find the average cost for removing between
75% and 80% of the chemical.
p
0
10
20
30
40
50
60
70
80
90
C
0
0.6
1
1.3
1.6
2
2.6
3.5
5.3
10.3
$470,000
$235,000
$117,500
$470,001
$940,000
____ 13. Evaluate the definite integral
.
a.
b.
c.
d.
e.
513
Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____
14.
Use substitution and partial fractions to find the indefinite integral.
.
a.
b.
c.
d.
e.
____ 15.
Find the area of the region bounded by the graphs of
, y = 0, x = 0,
and x = 1.
a.
A =
b.
A =
c.
A =
d.
A =
e.
A =
