Chapter 14 Switch The Order Integration And Show That

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14.1 Iterated Integrals and the Area in the Plane 819
14.1 Iterated Integrals and Area in the Plane
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the following integral.
a.
b.
c.
d.
e.
____ 2. Evaluate the following integral.
a.
b.
c.
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820 Chapter 14: Multiple Integration
d.
e.
____ 3. Evaluate the following integral.
a.
b.
c.
d.
e.
____ 4. Evaluate the following iterated integral.
a. 41.5
b. 38.5
c. 34.5
d. 33.5
e. 37.5
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14.1 Iterated Integrals and the Area in the Plane 821
____ 5. Evaluate the following iterated integral.
a.
b.
c.
d.
e.
____ 6. Evaluate the following iterated integral.
a. 5,901
b. 5,931
c. 5,955
d. 5,970
e. 6,017
____ 7. Evaluate the following iterated integral.
a.
b.
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822 Chapter 14: Multiple Integration
c.
d.
e.
____ 8. Evaluate the following improper integral.
a.
b.
c.
d.
e. The integral does not converge.
____ 9. Evaluate the improper iterated integral .
a.
b.
c.
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14.1 Iterated Integrals and the Area in the Plane 823
d.
e.
____ 10. Use an iterated integral to find the area of the region shown in the figure below.
a.
b.
c.
d.
e.
____ 11. Use an iterated integral to find the area of the region bounded by
.
a.
b.
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824 Chapter 14: Multiple Integration
c.
d.
e. The integral is improper and does not converge.
____ 12. Use an iterated integral to find the area of the region bounded by
.
a.
b.
c.
d.
e.
____ 13. Use an iterated integral to find the area of the region bounded by the graphs of the
equations and .
a.
b.
c.
d.
e.
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14.1 Iterated Integrals and the Area in the Plane 825
____ 14. Sketch the region R of integration and then switch the order of integration for the
following integral.
a.
b.
c.
d.
e.
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826 Chapter 14: Multiple Integration
____ 15. The area of a region R is given by the iterated integral . Switch the
order of integration and show that both orders yield the same area. What is this area?
a.
b.
c.
d.
e.
____ 16. The area of a region R is given by the iterated integrals .
Switch the order of integration and show that both orders yield the same area. What is this area?
a. 32
b. 1025
c. 64
d. 771
e. 63
____ 17. The area of a region R is given by the iterated integral . Switch the order
of integration and show that both orders yield the same area. What is this area?
a. 65
b. 16
c. 21
d. 8
e. 4
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14.1 Iterated Integrals and the Area in the Plane 827
____ 18. Evaluate the iterated integral below. Note that it is necessary to switch the order of
integration.
a.
b.
c.
d.
e.
____ 19. Evaluate the iterated integral by switching the order of
integration. Round your answer to three decimal places.
a. 0.538
b. 0.558
c. 30.538
d. 1.538
e. 4.538
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828 Chapter 14: Multiple Integration
14.1 Iterated Integrals and Area in the Plane
Answer Section
MULTIPLE CHOICE

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