Question 1

Convert the point   to rectangular coordinates (x,y,z).

Accepted Answer

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

Question 2

Evaluate the double integral.   R is bounded by y = 3x - 2, y = 3x + 1, y = -x + 2, and y = -x + 5

Accepted Answer

A)    
B)  -9 
C)    
D)  324 
A)    
B)  -9 
C)    
D)  324

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)  The integral can be evaluated only numerically. 
A)    
B)    
C)    
D)  The integral can be evaluated only numerically.

Question 5

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

Accepted Answer

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

Question 6

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)

Question 7

Evaluate the triple integral   .   ,

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Set up and evaluate the integral   where Q is the region above the xy-plane bounded by the hemisphere centered at (0,0,0) and with a radius of 4.

Accepted Answer

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

Question 12

Find the mass and moments of inertia Ix and Iy for a lamina in the shape of the region bounded by   and   with density   .

Accepted Answer

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

Question 13

Use a transformation to evaluate the double integral over the region R which is the region that lies inside   outside   and in the first quadrant.

Accepted Answer

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

Question 14

Convert the equation   into spherical coordinates.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Set up and evaluate the integral   where Q is the region inside a sphere centered at (0,0,0) and with a radius of 5.

Accepted Answer

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

Question 18

Write the equation   in cylindrical coordinates.

Accepted Answer

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

Question 19

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside   outside   and in the first quadrant.

Accepted Answer

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

Question 20

Compute the volume of the solid Q bounded by   and   .

Accepted Answer

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

Convert the point to rectangular coordinates (x,y,z).

Evaluate the double integral. R is bounded by y = 3x - 2, y = 3x + 1, y = -x + 2, and y = -x + 5

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

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

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

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

Evaluate the triple integral . ,

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

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

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

Set up and evaluate the integral where Q is the region above the xy-plane bounded by the hemisphere centered at (0,0,0) and with a radius of 4.

Find the mass and moments of inertia I_x and I_y for a lamina in the shape of the region bounded by and with density .

Use a transformation to evaluate the double integral over the region R which is the region that lies inside outside and in the first quadrant.

Convert the equation into spherical coordinates.

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

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

Set up and evaluate the integral where Q is the region inside a sphere centered at (0,0,0) and with a radius of 5.

Write the equation in cylindrical coordinates.

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside outside and in the first quadrant.

Compute the volume of the solid Q 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

Convert the point to rectangular coordinates (x,y,z).

Evaluate the double integral. R is bounded by y = 3x - 2, y = 3x + 1, y = -x + 2, and y = -x + 5

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

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

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

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

Evaluate the triple integral . ,

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

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

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

Set up and evaluate the integral where Q is the region above the xy-plane bounded by the hemisphere centered at (0,0,0) and with a radius of 4.

Find the mass and moments of inertia Ix and Iy for a lamina in the shape of the region bounded by and with density .

Use a transformation to evaluate the double integral over the region R which is the region that lies inside outside and in the first quadrant.

Convert the equation into spherical coordinates.

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

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

Set up and evaluate the integral where Q is the region inside a sphere centered at (0,0,0) and with a radius of 5.

Write the equation in cylindrical coordinates.

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside outside and in the first quadrant.

Compute the volume of the solid Q 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

Find the mass and moments of inertia I_x and I_y for a lamina in the shape of the region bounded by and with density .