Question 1

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.
-The coordinate axes and the line

Accepted Answer

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

Question 2

Evaluate the integral.
-

Accepted Answer

A)    $\pi$cos 3 
B)      cos 3 
C)      cos 3 
D)    $\pi$ cos 3 
A)    $\pi$cos 3 
B)      cos 3 
C)      cos 3 
D)    $\pi$ cos 3

Question 3

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.
-The curve   and the lines   and

Accepted Answer

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

Question 4

Find the Jacobian for the given transformation
-

Accepted Answer

A)    
B)  -   
C)  -27 
D)  27 
A)    
B)  -   
C)  -27 
D)  27

Question 5

Solve the problem.
-Write an iterated triple integral in the order   for the volume of the region in the first octant enclosed by the cylinder   and the plane   .

Accepted Answer

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

Question 6

Evaluate the integral.
-

Accepted Answer

A)  16 
B)  64 
C)  1024 
D)  256 
A)  16 
B)  64 
C)  1024 
D)  256

Question 7

Find the center of mass of a thin plate covering the given region with the given density function.
-The region between the curve y =   and the x-axis from x = 1 to x = 9, with density (x) =

Accepted Answer

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

Question 8

Evaluate the spherical coordinate integral.
-

Accepted Answer

A)    $\pi$ 
B)    $\pi$ 
C)  1944$\pi$ 
D)    $\pi$ 
A)    $\pi$ 
B)    $\pi$ 
C)  1944$\pi$ 
D)    $\pi$

Question 9

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)    $\pi$   
B)    $\pi$  
C)    $\pi$  
D)    $\pi$   
A)    $\pi$   
B)    $\pi$  
C)    $\pi$  
D)    $\pi$

Question 10

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)  3920   
B)      
C)  3136   
D)      
A)  3920   
B)      
C)  3136   
D)

Question 11

Find the average value of the function f over the given region.
-f(x, y) =   ; R = {(x, y): 1 $\le$ x $\le$ 3, 1 $\le$ y $\le$ 3}

Accepted Answer

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

Question 12

Solve the problem.
-Write an iterated triple integral in the order   for the volume of the rectangular solid in the first octant bounded by the planes   ,   , and   .

Accepted Answer

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

Question 13

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral
-

Accepted Answer

A)  - 1800 
B)  - 600 
C)  - 960 
D)  720 
A)  - 1800 
B)  - 600 
C)  - 960 
D)  720

Question 14

Evaluate the improper integral.
-

Accepted Answer

A)  243 
B)  486 
C)  405 
D)  324 
A)  243 
B)  486 
C)  405 
D)  324

Question 15

Evaluate the cylindrical coordinate integral.
-

Accepted Answer

A)  59,625 
B)  39,750 
C)    
D)    
A)  59,625 
B)  39,750 
C)    
D)

Question 16

Solve the problem.
-Find the centroid of the rectangular solid defined by   ,   ,   .

Accepted Answer

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

Question 17

Evaluate the cylindrical coordinate integral.
-

Accepted Answer

A)  1,380,000$\pi$ 
B)    $\pi$ 
C)  920,000$\pi$ 
D)  1,150,000$\pi$ 
A)  1,380,000$\pi$ 
B)    $\pi$ 
C)  920,000$\pi$ 
D)  1,150,000$\pi$

Question 18

Evaluate the integral.
-

Accepted Answer

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

Question 19

Evaluate the integral.
-

Accepted Answer

A)  16 
B)  50 
C)  32 
D)  25 
A)  16 
B)  50 
C)  32 
D)  25

Question 20

Solve the problem.
-Find the average height of the paraboloid   above the annular region   in the   .

Accepted Answer

A)    
B)    
C)  41 
D)    
A)    
B)    
C)  41 
D)

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. -The coordinate axes and the line

Evaluate the integral. -

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. -The curve and the lines and

Find the Jacobian for the given transformation -

Solve the problem. -Write an iterated triple integral in the order for the volume of the region in the first octant enclosed by the cylinder and the plane .

Evaluate the integral. -

Find the center of mass of a thin plate covering the given region with the given density function. -The region between the curve y = and the x-axis from x = 1 to x = 9, with density (x) =

Evaluate the spherical coordinate integral. -

Change the order of integration and evaluate the integral. -

Change the order of integration and evaluate the integral. -

Find the average value of the function f over the given region. -f(x, y) = $Find the average value of the function f over the given region. -f(x, y) = ; R = {(x, y): 1 \le x \le 3, 1 \le y \le 3}$ ; R = {(x, y): 1 $\le$ x $\le$ 3, 1 $\le$ y $\le$ 3}

Solve the problem. -Write an iterated triple integral in the order for the volume of the rectangular solid in the first octant bounded by the planes , , and .

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the improper integral. -

Evaluate the cylindrical coordinate integral. -

Solve the problem. -Find the centroid of the rectangular solid defined by , , .

Evaluate the cylindrical coordinate integral. -

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -Find the average height of the paraboloid above the annular region in the .

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Vector Calculus

Filters

Exam 16: Multiple Integration

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. -The coordinate axes and the line

Evaluate the integral. -

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. -The curve and the lines and

Find the Jacobian for the given transformation -

Solve the problem. -Write an iterated triple integral in the order for the volume of the region in the first octant enclosed by the cylinder and the plane .

Evaluate the integral. -

Find the center of mass of a thin plate covering the given region with the given density function. -The region between the curve y = and the x-axis from x = 1 to x = 9, with density (x) =

Evaluate the spherical coordinate integral. -

Change the order of integration and evaluate the integral. -

Change the order of integration and evaluate the integral. -

Find the average value of the function f over the given region. -f(x, y) = ; R = {(x, y): 1 ≤\le≤ x ≤\le≤ 3, 1 ≤\le≤ y ≤\le≤ 3}

Solve the problem. -Write an iterated triple integral in the order for the volume of the rectangular solid in the first octant bounded by the planes , , and .

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the improper integral. -

Evaluate the cylindrical coordinate integral. -

Solve the problem. -Find the centroid of the rectangular solid defined by , , .

Evaluate the cylindrical coordinate integral. -

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -Find the average height of the paraboloid above the annular region in the .

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Vector Calculus

Filters

Find the average value of the function f over the given region. -f(x, y) = $Find the average value of the function f over the given region. -f(x, y) = ; R = {(x, y): 1 \le x \le 3, 1 \le y \le 3}$ ; R = {(x, y): 1 $\le$ x $\le$ 3, 1 $\le$ y $\le$ 3}