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14.2 Double Integrals and Volume 829
14.2 Double Integrals and Volume
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate .
a. 3
b. 8
c. 6
d. 9
e. 5
____ 2. Evaluate . Round your answer to two decimal places.
a. 508.64
b. 307.25
c. 2457.99
d. 2224.97
e. 741.66
____ 3. Set up an integral for both orders of integration, and use the more convenient order to
evaluate the integral below over the region R.
a.
b.
c.
d.
e.
830 Chapter 14: Multiple Integration
____ 4. Use a double integral to find the volume of the indicated solid.
a. 32
b. 16
c. 60
d. 15
e. 24
____ 5. Use a double integral to find the volume of the indicated solid.
a.
b.
14.2 Double Integrals and Volume 831
c.
d.
e.
____ 6. Use a double integral to find the volume of the indicated solid.
a.
b.
c.
d.
e. none of the above
832 Chapter 14: Multiple Integration
____ 7. Use a double integral to find the volume of the indicated solid.
a. 16
b. 9
c. 4
d. 20
e. 6
____ 8. Set up and evaluate a double integral to find the volume of the solid bounded by the
graphs of the equations given below.
a.
b.
c.
d.
e.
14.2 Double Integrals and Volume 833
____ 9. Set up and evaluate a double integral to find the volume of the solid bounded by the
graphs of the equations and .
a. 1,089
b. 35,937
c. 35,949
d. 11,979
e. 2,178
____ 10. Set up and evaluate a double integral to find the volume of the solid bounded by the
graphs of the equations and in the first octant.
a. 5,184
b. 576
c. 3,456
d. 1,728
e. 1,152
____ 11. Set up and evaluate a double integral to find the volume of the solid bounded by the
graphs of the equations given below.
a.
b.
c.
d.
e.
834 Chapter 14: Multiple Integration
____ 12. Evaluate the iterated integral below. Note that it is necessary to switch the order of
integration.
a.
b.
c.
d.
e.
____ 13. Evaluate the integral by switching the order of
integration. Round your answer to two decimal places.
a. 12.39
b. 19.36
c. 9.73
d. 7.73
e. 26.57
____ 14. Find the average value of over the region R where:
R: rectangle with vertices
a.
b.
14.2 Double Integrals and Volume 835
c.
d.
e.
____ 15. Find the average value of over the region R, where R is a triangle
with vertices .
a.
b.
c.
d.
e.
____ 16. Suppose the Cobb-Douglas production function for an automobile manufacturer is
where x is the number of units of labor and y is the number of units of capital.
Estimate the average production level if the number of units of labor x varies between 150 and 200
and the number of units of capital y varies between 375 and 450. Round your answer to two decimal
places.
a. 229,894.96
b. 15,558.45
c. 55,174.79
d. 24,631.60
e. 5,971.30
836 Chapter 14: Multiple Integration
____ 17. Suppose the temperature in degrees Celsius on the surface of a metal plate is
where x and y are measured in centimeters. Estimate the average temperature
if x varies between 0 and 2 centimeters and y varies between 0 and 7 centimeters.
a. degrees Celsius
b. degrees Celsius
c. degrees Celsius
d. degrees Celsius
e. degrees Celsius
14.2 Double Integrals and Volume 837
14.2 Double Integrals and Volume
Answer Section
MULTIPLE CHOICE
