Question 1

Evaluate the triple integral   where Q is the bounded by         and

Accepted Answer

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

Question 2

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 3

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

Accepted Answer

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

Question 4

Use polar coordinates to evaluate   where R is the disk   .

Accepted Answer

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

Question 5

Evaluate the triple integral   .   ,

Accepted Answer

A)  4 
B)    
C)  0 
D)    
A)  4 
B)    
C)  0 
D)

Question 6

Evaluate the iterated integral by first changing the order of integration.

Accepted Answer

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

Question 7

Evaluate the integral   , where Q is the region with z > 0 bounded by   and   .

Accepted Answer

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

Question 8

Use polar coordinates to evaluate   where R is the disk   .

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the surface area of the portion of   above the xy plane.

Accepted Answer

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

Question 11

Find a transformation from a rectangular region S in the uv-plane to the region R which is bounded by   and

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Rewrite the iterated integral by iterating in the order

Accepted Answer

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

Question 14

Write the equation   in cylindrical coordinates.

Accepted Answer

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

Question 15

Evaluate the iterated integral.

Accepted Answer

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

Question 16

Evaluate the double integral.

Accepted Answer

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

Question 17

Find the surface area of   between   ,   and   .

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Evaluate   by converting to polar coordinates.

Accepted Answer

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

Question 20

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

Accepted Answer

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

Evaluate the triple integral where Q is the bounded by and

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

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

Use polar coordinates to evaluate where R is the disk .

Evaluate the triple integral . ,

Evaluate the iterated integral by first changing the order of integration.

Evaluate the integral , where Q is the region with z > 0 bounded by and .

Use polar coordinates to evaluate where R is the disk .

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

Find the surface area of the portion of above the xy plane.

Find a transformation from a rectangular region S in the uv-plane to the region R which is bounded by and

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

Rewrite the iterated integral by iterating in the order

Write the equation in cylindrical coordinates.

Evaluate the iterated integral.

Evaluate the double integral.

Find the surface area of between , and .

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

Evaluate by converting to polar coordinates.

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

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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

Exam 15: Multiple Integrals

Evaluate the triple integral where Q is the bounded by and

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

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

Use polar coordinates to evaluate where R is the disk .

Evaluate the triple integral . ,

Evaluate the iterated integral by first changing the order of integration.

Evaluate the integral , where Q is the region with z > 0 bounded by and .

Use polar coordinates to evaluate where R is the disk .

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

Find the surface area of the portion of above the xy plane.

Find a transformation from a rectangular region S in the uv-plane to the region R which is bounded by and

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

Rewrite the iterated integral by iterating in the order

Write the equation in cylindrical coordinates.

Evaluate the iterated integral.

Evaluate the double integral.

Find the surface area of between , and .

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

Evaluate by converting to polar coordinates.

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

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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