Larson_Calculus_10e ch14sec02
MULTIPLE CHOICE
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.
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.
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
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.
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.
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.
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
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