Deck 14: Section 2: Multiple Integration

Question 1

Find the average value of over the region R where: R: rectangle with vertices

A)
B)
C)
D)
E)

Answer 1

Question 2

Use a double integral to find the volume of the indicated solid.

A)
B)
C)
D)
E)

Answer 2

Question 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)

Answer 3

Question 4

Use a double integral to find the volume of the indicated solid.

A) 16
B) 9
C) 4
D) 20
E) 6

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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)

Question 10

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)

Question 11

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

Question 12

Find the average value of over the region R, where R is a triangle with vertices .

A)
B)
C)
D)
E)

Question 13

Use a double integral to find the volume of the indicated solid.

A)
B)
C)
D)
E) none of the above

Question 14

Evaluate . Round your answer to two decimal places.

A) 508.64
B) 307.25
C) 2457.99
D) 2224.97
E) 741.66

Question 15

Evaluate the iterated integral below. Note that it is necessary to switch the order of integration.

A)
B)
C)
D)
E)

Question 16

Use a double integral to find the volume of the indicated solid.

A) 32
B) 16
C) 60
D) 15
E) 24

Question 17

Find the volume of the solid region bounded by the graphs of the equations . (Hint: You may need to use Wallis's Formula.). Round your answer to two decimal places.

A) 9.26
B) 32.21
C) 29.09
D) 58.18
E) 18.52

Question 18

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)

Question 19

Evaluate .

A) 3
B) 8
C) 6
D) 9
E) 5