Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) 12.39 
B) 19.36 
C) 9.73 
D) 7.73 
E) 26.57 
A) 12.39 
B) 19.36 
C) 9.73 
D) 7.73 
E) 26.57

Question 3

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

Accepted Answer

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

Question 4

Evaluate the following iterated integral.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Evaluate the following iterated integral.

Accepted Answer

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

Question 7

Evaluate the following improper integral.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Evaluate the following iterated integral.

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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 14

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

Accepted Answer

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

Question 15

Evaluate the improper iterated integral

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   in the first octant.

Accepted Answer

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

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

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

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

Evaluate the following iterated integral.

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

Evaluate the following iterated integral.

Evaluate the following improper integral.

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

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

Evaluate the following iterated integral.

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

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

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

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

Evaluate the improper iterated integral

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.

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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Exam 14: Multiple Integration

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

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

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

Evaluate the following iterated integral.

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

Evaluate the following iterated integral.

Evaluate the following improper integral.

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

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

Evaluate the following iterated integral.

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

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

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

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

Evaluate the improper iterated integral

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.

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

Filters