Question 1

Evaluate the iterated integral   by changing coordinate systems.

Accepted Answer

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

Question 2

Convert the equation   into spherical coordinates.

Accepted Answer

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

Question 3

Find the mass and the center of mass of the lamina bounded by   and   with density   .

Accepted Answer

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

Question 4

Evaluate the iterated integral.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Compute the Riemann sum for the given function, the irregular partition shown and midpoint evaluation.

Accepted Answer

A)  69 
B)  40 
C)  -66 
D)  66 
A)  69 
B)  40 
C)  -66 
D)  66

Question 8

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

Accepted Answer

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

Question 9

Evaluate the triple integral   .   ,

Accepted Answer

A)  8 
B)    
C)  0 
D)    
A)  8 
B)    
C)  0 
D)

Question 10

Change the order of integration.

Accepted Answer

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

Question 11

Evaluate the triple integral   .   ,

Accepted Answer

A)    
B)  2 
C)    
D)    
A)    
B)  2 
C)    
D)

Question 12

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 + 4, y = 4x + 7, y = -x + 2, and y = -x + 4

Accepted Answer

Answer details may vary.
The r

Evaluate the iterated integral by changing coordinate systems.

Convert the equation into spherical coordinates.

Find the mass and the center of mass of the lamina bounded by and with density .

Evaluate the iterated integral.

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

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

Compute the Riemann sum for the given function, the irregular partition shown and midpoint evaluation.

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

Evaluate the triple integral . ,

Change the order of integration.

Evaluate the triple integral . ,

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 + 4, y = 4x + 7, y = -x + 2, and y = -x + 4

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

Exam 14: Multiple Integrals

Evaluate the iterated integral by changing coordinate systems.

Convert the equation into spherical coordinates.

Find the mass and the center of mass of the lamina bounded by and with density .

Evaluate the iterated integral.

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

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

Compute the Riemann sum for the given function, the irregular partition shown and midpoint evaluation.

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

Evaluate the triple integral . ,

Change the order of integration.

Evaluate the triple integral . ,

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 + 4, y = 4x + 7, y = -x + 2, and y = -x + 4

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