Question 1

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

Accepted Answer

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

Question 2

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?

Accepted Answer

A) 32 
B) 1025 
C) 64 
D) 771 
E) 63 
A) 32 
B) 1025 
C) 64 
D) 771 
E) 63 C

Question 3

Evaluate   Round your answer to two decimal places.

Accepted Answer

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

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

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?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

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.

Accepted Answer

A)    degrees Celsius 
B)    degrees Celsius 
C)    egrees Celsius 
D)    degrees Celsius 
E)    degrees Celsius 
A)    degrees Celsius 
B)    degrees Celsius 
C)    egrees Celsius 
D)    degrees Celsius 
E)    degrees Celsius

Question 7

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?

Accepted Answer

A) 65 
B) 16 
C) 21 
D) 8 
E) 4 
A) 65 
B) 16 
C) 21 
D) 8 
E) 4

Question 8

Evaluate

Accepted Answer

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

Question 9

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

Accepted Answer

A) 1,089 
B) 35,937 
C) 35,949 
D) 11,979 
E) 2,178 
A) 1,089 
B) 35,937 
C) 35,949 
D) 11,979 
E) 2,178

Question 10

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.

Accepted Answer

A) 229,894.96 
B) 15,558.45 
C) 55,174.79 
D) 24,631.60 
E) 5,971.30 
A) 229,894.96 
B) 15,558.45 
C) 55,174.79 
D) 24,631.60 
E) 5,971.30

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Evaluate the following iterated integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Evaluate the following integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Evaluate the following integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Evaluate the following integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Evaluate the iterated integral   by switching the order of integration.Round your answer to three decimal places.

Accepted Answer

A) 0.538 
B) 0.558 
C) 30.538 
D) 1.538 
E) 4.538 
A) 0.538 
B) 0.558 
C) 30.538 
D) 1.538 
E) 4.538

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

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?

Evaluate Round your answer to two decimal places.

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

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?

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.

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?

Evaluate

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

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

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

Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.

Evaluate the following iterated integral.

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

Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.

Evaluate the following integral.

Evaluate the following integral.

Evaluate the following integral.

Evaluate the iterated integral by switching the order of integration.Round your answer to three decimal places.

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Integration Techniques, Lhôpitals Rule, and Improper Integrals

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Exam 14: Multiple Integration

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

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?

Evaluate Round your answer to two decimal places.

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

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?

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.

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?

Evaluate

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

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

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

Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.

Evaluate the following iterated integral.

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

Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.

Evaluate the following integral.

Evaluate the following integral.

Evaluate the following integral.

Evaluate the iterated integral by switching the order of integration.Round your answer to three decimal places.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

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