Question 1

Set up the triple integral   in cylindrical coordinates where Q is the solid above   below   and inside

Accepted Answer

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

Question 2

Evaluate the iterated integral.

Accepted Answer

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

Question 3

Use polar coordinates to evaluate   where R is the disk   .

Accepted Answer

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

Question 4

Change the order of integration.

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D)

Question 5

Evaluate the triple integral   where Q is the bounded by         and

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D)    
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D)

Question 6

Set up and evaluate the integral   where Q is the region inside a sphere centered at (0,0,0) and with a radius of 7.

Accepted Answer

A)    
B)  0 
C)    
D)    
A)    
B)  0 
C)    
D)

Question 7

Find the Jacobian of the given transformation.

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

Question 8

Use polar coordinates to evaluate   where R is the disk   .

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

Question 9

Find the volume of the solid bounded by the given surfaces.

Accepted Answer

A)    
B)    
C)  40 
D)    
A)    
B)    
C)  40 
D)

Question 10

Calculate the mass of an object with density   and bounded by   and

Accepted Answer

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

Question 11

Evaluate the triple integral.

Accepted Answer

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

Question 12

Compute the volume of the solid bounded by   ,   and the coordinate planes.

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

Question 13

Find the center of mass of the solid with density   and the given shape.   ,

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B)    
C)    
D)    
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C)    
D)

Question 14

Use a transformation to evaluate the double integral over the region R which is bounded by   and

Accepted Answer

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

Question 15

Using an appropriate coordinate system, evaluate the integral   where Q is the region inside the cylinder   and between the planes   and   .

Accepted Answer

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

Question 16

Convert the equation   in spherical coordinates to an equation in rectangular coordinates.

Accepted Answer

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

Question 17

Approximate the double integral.   , where R is bounded by x = 0, x = 3, y = 0, and y = x + 2

Accepted Answer

A)  2.636 
B)  2.658 
C)  0.886 
D)  1.772 
A)  2.636 
B)  2.658 
C)  0.886 
D)  1.772

Question 18

Use an appropriate coordinate system to compute the volume of the solid below   and above   .

Accepted Answer

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

Question 19

Find the Jacobian of the given transformation.

Accepted Answer

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

Question 20

Which of the following could represent the triple integral   in cylindrical coordinates where Q is the region bounded below by   and above by   ?

Accepted Answer

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

Set up the triple integral in cylindrical coordinates where Q is the solid above below and inside

Evaluate the iterated integral.

Use polar coordinates to evaluate where R is the disk .

Change the order of integration.

Evaluate the triple integral where Q is the bounded by and

Set up and evaluate the integral where Q is the region inside a sphere centered at (0,0,0) and with a radius of 7.

Find the Jacobian of the given transformation.

Use polar coordinates to evaluate where R is the disk .

Find the volume of the solid bounded by the given surfaces.

Calculate the mass of an object with density and bounded by and

Evaluate the triple integral.

Compute the volume of the solid bounded by , and the coordinate planes.

Find the center of mass of the solid with density and the given shape. ,

Use a transformation to evaluate the double integral over the region R which is bounded by and

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Convert the equation in spherical coordinates to an equation in rectangular coordinates.

Approximate the double integral. , where R is bounded by x = 0, x = 3, y = 0, and y = x + 2

Use an appropriate coordinate system to compute the volume of the solid below and above .

Find the Jacobian of the given transformation.

Which of the following could represent the triple integral in cylindrical coordinates where Q is the region bounded below by and above by ?

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

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Exam 14: Multiple Integrals

Set up the triple integral in cylindrical coordinates where Q is the solid above below and inside

Evaluate the iterated integral.

Use polar coordinates to evaluate where R is the disk .

Change the order of integration.

Evaluate the triple integral where Q is the bounded by and

Set up and evaluate the integral where Q is the region inside a sphere centered at (0,0,0) and with a radius of 7.

Find the Jacobian of the given transformation.

Use polar coordinates to evaluate where R is the disk .

Find the volume of the solid bounded by the given surfaces.

Calculate the mass of an object with density and bounded by and

Evaluate the triple integral.

Compute the volume of the solid bounded by , and the coordinate planes.

Find the center of mass of the solid with density and the given shape. ,

Use a transformation to evaluate the double integral over the region R which is bounded by and

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Convert the equation in spherical coordinates to an equation in rectangular coordinates.

Approximate the double integral. , where R is bounded by x = 0, x = 3, y = 0, and y = x + 2

Use an appropriate coordinate system to compute the volume of the solid below and above .

Find the Jacobian of the given transformation.

Which of the following could represent the triple integral in cylindrical coordinates where Q is the region bounded below by and above by ?

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

Filters