8.1 Basic Integration Rules
474
8.1 Basic Integration Rules
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 3. Find the indefinite integral.
a.
b.
475 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
c.
d.
e.
____ 4. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 6. Find the indefinite integral .
a.
b.
c.
d.
8.1 Basic Integration Rules
476
e.
____ 7. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 9. Find the indefinite integral .
a.
b.
c.
d.
e.
477 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 10. Solve the differential equation .
a.
b.
c.
d.
e.
____ 11.
Solve the differential equation
.
a.
b.
c.
d.
e.
____ 12. Evaluate the definite integral .
4
7
5
0
8
8.1 Basic Integration Rules
478
____ 13. Find the definite integral.
64
56
8
104
7
____ 14. Find the definite integral.
a.
b.
c.
d.
e.
____ 15. Find the indefinite integral.
a.
b.
c.
479 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
d.
e.
8.1 Basic Integration Rules
480
8.1 Basic Integration Rules
Answer Section
481 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.2 Integration by Parts
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 3. Find the indefinite integral.
a.
b.
8.2 Integration by Parts
482
c.
d.
e.
____ 4. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral.
a.
b.
c.
d.
483
Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
e.
____
6.
Find the indefinite integral.
a.
b.
c.
d.
e.
____ 7. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral.
a.
8.2 Integration by Parts
484
b.
c.
d.
e.
____ 9. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 10. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 11. Solve .
485 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
a.
b.
c.
d.
e.
____ 12. Find the definite integral.
a.
b.
c.
d.
e.
____ 13. Evaluate . Round your answer to three decimal places.
a.
b.
c.
8.2 Integration by Parts
486
d.
e.
____ 14. Find .
a.
b.
c.
d.
e.
____ 15. Suppose a damping force affects the vibration of a spring so that the displacement of
the string is given by . Find the average value of y on the interval from
to . Round your answer to three decimal places.
0.406
0.131
0.122
0.129
0.382
____
16.
Suppose a model for the ability M of a child to memorize, measured on a scale from
to
, is given by
where t is the child’s age in years. Find the average
value of this model between the child’s first and second birthdays. Round your answer to three
decimal places.
a. 1.891
487 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
0.920
1.541
3.991
3.026
8.2 Integration by Parts
488
8.2 Integration by
Parts Answer Section
489 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.3 Trigonometric Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 3. Find the indefinite integral.
a.
b.
8.3 Trigonometric Integrals
490
c.
d.
e.
____ 4. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral.
a.
b.
c.
d.
e.
491 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 6. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 7. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral.
a.
8.3 Trigonometric Integrals
492
b.
c.
d.
e.
____ 9. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 10. Find the indefinite integral.
a.
b.
c.
d.
e.
493 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.
____ 13. Find the indefinite integral.
a.
b.