Question 1

Evaluate the triple integral.

Accepted Answer

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

Question 2

Evaluate the iterated integral.

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D)    
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D)

Question 3

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

Accepted Answer

A)    
B)    
C)  117 
D)  351 
A)    
B)    
C)  117 
D)  351

Question 4

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

Accepted Answer

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B)    
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D)    
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D)

Question 5

Evaluate the iterated integral   by changing coordinate systems.

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D)

Question 6

Use an appropriate coordinate system to find the volume of a solid bounded by   .

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D)    
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D)

Question 7

Use an appropriate coordinate system to find the volume of the solid lying along the positive z-axis and bounded by the cone   and the sphere   .

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D)

Question 8

A skydiving club is having a competition to see who can land the closest to a target point. Jeff is a highly experienced skydiver, and the probability that he will land inside a region R is given by   , where the coordinate system is centered on the target point. Compute the probability that Jeff lands within 11 feet of the target point.

Accepted Answer

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D)    
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D)

Question 9

Find the surface area of the portion of the surface   in the first octant.

Accepted Answer

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D)    
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Question 10

Compute the volume of the solid bounded by the given surfaces.   and the three coordinate planes

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C)    
D)    
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D)

Question 11

Change the order of integration.

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Question 12

Use a double integral to find the area of the region bounded by   ,   and   .

Accepted Answer

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D)    
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D)

Question 13

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

Accepted Answer

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D)    
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D)

Question 14

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

Accepted Answer

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B)    
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D)    
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D)

Question 15

Using an appropriate coordinate system, evaluate the integral   where Q is the region above z = 0 bounded by the cone   and the sphere   .

Accepted Answer

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

Question 16

Evaluate the iterated integral   by changing coordinate systems.

Accepted Answer

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

Question 17

Find the surface area of the portion of   above   .

Accepted Answer

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D)    
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B)    
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D)

Question 18

Compute the Riemann sum for the given function and region, a partition with n equal-sized rectangles and the given evaluation rule.

Accepted Answer

A)  -8 
B)  8 
C)  0 
D)  -36 
A)  -8 
B)  8 
C)  0 
D)  -36

Question 19

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work.
R is bounded by y = 4x + 5, y = 4x + 6, y = -2x + 2, and y = -2x + 5

Accepted Answer

Answer details may vary.
The r

Question 20

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)

Evaluate the triple integral.

Evaluate the iterated integral.

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

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

Evaluate the iterated integral by changing coordinate systems.

Use an appropriate coordinate system to find the volume of a solid bounded by .

Use an appropriate coordinate system to find the volume of the solid lying along the positive z-axis and bounded by the cone and the sphere .

Find the surface area of the portion of the surface in the first octant.

Compute the volume of the solid bounded by the given surfaces. and the three coordinate planes

Change the order of integration.

Use a double integral to find the area of the region bounded by , and .

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

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

Using an appropriate coordinate system, evaluate the integral where Q is the region above z = 0 bounded by the cone and the sphere .

Evaluate the iterated integral by changing coordinate systems.

Find the surface area of the portion of above .

Compute the Riemann sum for the given function and region, a partition with n equal-sized rectangles and the given evaluation rule.

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work. R is bounded by y = 4x + 5, y = 4x + 6, y = -2x + 2, and y = -2x + 5

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

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.

Evaluate the iterated integral.

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

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

Evaluate the iterated integral by changing coordinate systems.

Use an appropriate coordinate system to find the volume of a solid bounded by .

Use an appropriate coordinate system to find the volume of the solid lying along the positive z-axis and bounded by the cone and the sphere .

Find the surface area of the portion of the surface in the first octant.

Compute the volume of the solid bounded by the given surfaces. and the three coordinate planes

Change the order of integration.

Use a double integral to find the area of the region bounded by , and .

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

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

Using an appropriate coordinate system, evaluate the integral where Q is the region above z = 0 bounded by the cone and the sphere .

Evaluate the iterated integral by changing coordinate systems.

Find the surface area of the portion of above .

Compute the Riemann sum for the given function and region, a partition with n equal-sized rectangles and the given evaluation rule.

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work. R is bounded by y = 4x + 5, y = 4x + 6, y = -2x + 2, and y = -2x + 5

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

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