500 Chapter 8: Integration Techniques, L’H pital’s Rule, and Improper Integrals
8.8 Improper Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____ 2. Determine whether the improper integral diverges or converges. Evaluate the
integral if it converges.
a.
b.
c.
d.
e. diverges
____ 3. Determine whether the improper integral diverges or converges. Evaluate
the integral if it converges.
a.
b.
c.
d.
e. diverges
ô
8.8 Improper Integrals 501
____ 4. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a. 18
b. 9
c.
d. 3
e. diverges
____ 5. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____ 6. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
____ 7. Determine whether the improper integral diverges or converges.
a.
b.
502 Chapter 8: Integration Techniques, L’H pital’s Rule, and Improper Integrals
____ 8. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____ 9. Determine whether the improper integral diverges or converges.
a.
b.
____ 10. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____ 11. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c. diverges
ô
8.8 Improper Integrals 503
d.
e.
____ 12. Find the area between the x-axis and the graph of the function .
a.
b.
c.
d.
e.
____ 13. Suppose the capitalized cost C is given by where is the
original investment, t is the time in years, r is the annual interest rate compounded continuously, and
is the annual cost of maintenance. Find the capitalized cost C of an asset forever if
. Round your answer to the nearest dollar.
a.
b.
c.
d.
e.
504 Chapter 8: Integration Techniques, L’H pital’s Rule, and Improper Integrals
____ 14. Suppose the capitalized cost C is given by where is the
original investment, t is the time in years, r is the annual interest rate compounded continuously, and
is the annual cost of maintenance. Find the capitalized cost C of an asset forever if
. Round your answer to the nearest dollar.
a. 681,400
b. 1,753,400
c. 1,799,511
d. 681,420
e.
____ 15. Determine whether the improper integral diverges or converges. Evaluate the
integral if it converges.
a. 3
b. 2
c. 1
d.
e. diverges
ô
8.8 Improper Integrals 505
8.8 Improper Integrals
Answer Section