Question 1

Evaluate the integral.
-

Accepted Answer

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

Question 2

Use spherical coordinates to find the volume of the indicated region.
-the region inside the solid sphere   that lies between the cones   and

Accepted Answer

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

Question 3

Evaluate the double integral over the given region.
-  R = {(x, y): 0$\le$x$\le$1, 0$\le$y$\le$1}

Accepted Answer

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

Question 4

Use spherical coordinates to find the volume of the indicated region.
-the region enclosed by the cone   between the planes   and

Accepted Answer

A)  312$\pi$ 
B)  312 
C)  234 
D)  234$\pi$ 
A)  312$\pi$ 
B)  312 
C)  234 
D)  234$\pi$

Question 5

Write an equivalent double integral with the order of integration reversed.
-

Accepted Answer

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

Question 6

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

Accepted Answer

A)  8$\pi$ 
B)  4$\pi$ 
C)  9$\pi$ 
D)  5$\pi$ 
A)  8$\pi$ 
B)  4$\pi$ 
C)  9$\pi$ 
D)  5$\pi$

Question 7

Evaluate the integral.
-

Accepted Answer

A)    
B)    
C)    
D)  36 
A)    
B)    
C)    
D)  36

Question 8

Solve the problem.
-Rewrite the integral   in the order   .

Accepted Answer

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

Question 9

Find the Jacobian for the given transformation
-x = 4u cosh 8v, y = 4u sinh 8v

Accepted Answer

A)  128v 
B)  256u 
C)  128u 
D)  256v 
A)  128v 
B)  256u 
C)  128u 
D)  256v

Question 10

Provide an appropriate response.
-What does the graph of the equation   look like?

Accepted Answer

A)  The xz-plane 
B)  The x-axis 
C)  The y-axis 
D)  The yz-plane 
A)  The xz-plane 
B)  The x-axis 
C)  The y-axis 
D)  The yz-plane

Question 11

Use the given transformation to evaluate the integral.
-  where R is the interior of the ellipsoid

Accepted Answer

A)     $\pi$ 
B)  42 $\pi$ 
C)     $\pi$ 
D)     $\pi$ 
A)     $\pi$ 
B)  42 $\pi$ 
C)     $\pi$ 
D)     $\pi$

Question 12

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

Accepted Answer

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

Question 13

Solve the problem.
-Write an iterated triple integral in the order   for the volume of the tetrahedron cut from the first octant by the plane   .

Accepted Answer

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

Question 14

Evaluate the improper integral.
-

Accepted Answer

A)  48(1 - ln 2) 
B)  576(1 - ln 2) 
C)  288(1 - ln 2) 
D)  96(1 - ln 2) 
A)  48(1 - ln 2) 
B)  576(1 - ln 2) 
C)  288(1 - ln 2) 
D)  96(1 - ln 2)

Question 15

Solve the problem.
-Rewrite the integral   in the order   .

Accepted Answer

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

Question 16

Evaluate the integral by changing the order of integration in an appropriate way.
-

Accepted Answer

A)  8 ln 2 ln cos 6 
B)  8 ln 4 ln cos 6 
C)  - 8 ln 4 ln cos 6 
D)  - 8 ln 2 ln cos 6 
A)  8 ln 2 ln cos 6 
B)  8 ln 4 ln cos 6 
C)  - 8 ln 4 ln cos 6 
D)  - 8 ln 2 ln cos 6

Question 17

Evaluate the integral.
-

Accepted Answer

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

Question 18

Reverse the order of integration and then evaluate the integral.
-

Accepted Answer

A)      
B)    (1 - cos 49) 
C)      
D)    (1 - cos 49) 
A)      
B)    (1 - cos 49) 
C)      
D)    (1 - cos 49)

Question 19

Solve the problem.
-Find the average distance from a point   in the region bounded by   to the origin.

Accepted Answer

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

Question 20

Reverse the order of integration and then evaluate the integral.
-

Accepted Answer

A)      
B)    (   - 1) 
C)    (   - 1) 
D)      
A)      
B)    (   - 1) 
C)    (   - 1) 
D)

Evaluate the integral. -

Use spherical coordinates to find the volume of the indicated region. -the region inside the solid sphere that lies between the cones and

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = {(x, y): 0 \le x \le 1, 0 \le y \le 1}$ R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

Use spherical coordinates to find the volume of the indicated region. -the region enclosed by the cone between the planes and

Write an equivalent double integral with the order of integration reversed. -

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

Evaluate the integral. -

Solve the problem. -Rewrite the integral in the order .

Find the Jacobian for the given transformation -x = 4u cosh 8v, y = 4u sinh 8v

Provide an appropriate response. -What does the graph of the equation look like?

Use the given transformation to evaluate the integral. - where R is the interior of the ellipsoid

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

Solve the problem. -Write an iterated triple integral in the order for the volume of the tetrahedron cut from the first octant by the plane .

Evaluate the improper integral. -

Solve the problem. -Rewrite the integral in the order .

Evaluate the integral by changing the order of integration in an appropriate way. -

Evaluate the integral. -

Reverse the order of integration and then evaluate the integral. -

Solve the problem. -Find the average distance from a point in the region bounded by to the origin.

Reverse the order of integration and then evaluate the integral. -

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

Evaluate the integral. -

Use spherical coordinates to find the volume of the indicated region. -the region inside the solid sphere that lies between the cones and

Evaluate the double integral over the given region. - R = {(x, y): 0 ≤\le≤ x ≤\le≤ 1, 0 ≤\le≤ y ≤\le≤ 1}

Use spherical coordinates to find the volume of the indicated region. -the region enclosed by the cone between the planes and

Write an equivalent double integral with the order of integration reversed. -

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

Evaluate the integral. -

Solve the problem. -Rewrite the integral in the order .

Find the Jacobian for the given transformation -x = 4u cosh 8v, y = 4u sinh 8v

Provide an appropriate response. -What does the graph of the equation look like?

Use the given transformation to evaluate the integral. - where R is the interior of the ellipsoid

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

Solve the problem. -Write an iterated triple integral in the order for the volume of the tetrahedron cut from the first octant by the plane .

Evaluate the improper integral. -

Solve the problem. -Rewrite the integral in the order .

Evaluate the integral by changing the order of integration in an appropriate way. -

Evaluate the integral. -

Reverse the order of integration and then evaluate the integral. -

Solve the problem. -Find the average distance from a point in the region bounded by to the origin.

Reverse the order of integration and then evaluate the integral. -

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

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = {(x, y): 0 \le x \le 1, 0 \le y \le 1}$ R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}