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454 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 455
c.
d.
e.
____ 4. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral.
a.
b.
c.
d.
e.
456 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.
b.
c.
8.2 Integration by Parts 457
d.
e.
____ 9. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 10. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 11. Solve .
a.
b.
458 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
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.
d.
e.
8.2 Integration by Parts 459
____ 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.
a. 0.406
b. 0.131
c. 0.122
d. 0.129
e. 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
b. 0.920
c. 1.541
d. 3.991
e. 3.026
460 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.2 Integration by Parts
Answer Section
