Deck 14: Multiple Integration

Question 1

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Answer 1

Question 2

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Answer 2

Question 3

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)

Answer 3

Question 4

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

Question 5

Evaluate the following improper integral.

A)
B)
C)
D)
E)The integral does not converge.

Question 6

Evaluate the following iterated integral.

A)41.5
B)38.5
C)34.5
D)33.5
E)37.5

Question 7

Use an iterated integral to find the area of the region bounded by the graphs of the equations

A)
B)
C)
D)
E)

Question 8

Sketch the region R of integration and then switch the order of integration for the following integral.

A)
B)
C)
D)
E)

Question 9

Evaluate

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

Question 10

Evaluate the following integral.

A)
B)
C)
D)
E)

Question 11

Evaluate the following iterated integral.

A)5,901
B)5,931
C)5,955
D)5,970
E)6,017

Question 12

Evaluate the following integral.

A)
B)
C)
D)
E)

Question 13

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

Question 14

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

Question 15

Evaluate the improper iterated integral

A)
B)
C)
D)
E)

Question 16

Evaluate the following integral.

A)
B)
C)
D)
E)

Question 17

Use an iterated integral to find the area of the region bounded by

A)
B)
C)
D)
E)

Question 18

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

A)
B)
C)
D)
E)

Question 19

Use an iterated integral to find the area of the region bounded by

A)
B)
C)
D)
E)The integral is improper and does not converge.

Question 20

Use an iterated integral to find the area of the region shown in the figure below.

A)
B)
C)
D)
E)

Question 21

Evaluate Round your answer to two decimal places.

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

Question 22

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

A)
B)
C)
D)
E)

Question 23

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

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

Question 24

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 25

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

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

Question 26

Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations in the first octant.

A)5,184
B)576
C)3,456
D)1,728
E)1,152

Question 27

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

A)
B)
C)
D)
E)

Question 28

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 29

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

A)
B)
C)
D)
E)

Question 30

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 31

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) egrees Celsius
D) degrees Celsius
E) degrees Celsius

Question 32

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 33

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

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

Question 34

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

A)
B)
C)
D)
E)

Question 35

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 36

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