Question 1

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
-

Accepted Answer

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

Question 2

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 3

Solve the problem.
-Find the center of mass of the hemisphere of constant density bounded   and the

Accepted Answer

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

Question 4

Find the volume of the indicated region.
-the region that lies under the plane   and above the square

Accepted Answer

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

Question 5

Evaluate the spherical coordinate integral.
-

Accepted Answer

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

Question 6

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

Accepted Answer

A)  A cylinder 
B)  A line 
C)  A sphere 
D)  A plane 
A)  A cylinder 
B)  A line 
C)  A sphere 
D)  A plane

Question 7

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

Accepted Answer

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

Question 8

Solve the problem.
-Let D be the region that is bounded below by the cone   and above by the sphere   Set up the triple integral for the volume of D in spherical coordinates.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Evaluate the integral.
-

Accepted Answer

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

Question 11

Evaluate the cylindrical coordinate integral.
-

Accepted Answer

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

Question 12

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
-

Accepted Answer

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

Question 13

Find the volume of the indicated region.
-the region bounded by the cylinder   and the planes   and

Accepted Answer

A)  80$\pi$ 
B)  400$\pi$ 
C)  100$\pi$ 
D)  20$\pi$ 
A)  80$\pi$ 
B)  400$\pi$ 
C)  100$\pi$ 
D)  20$\pi$

Question 14

Use cylindrical coordinates to find the volume of the indicated region.
-the region bounded by the cylinders     and the planes

Accepted Answer

A)  144$\pi$ 
B)  576$\pi$ 
C)  288$\pi$ 
D)  432$\pi$ 
A)  144$\pi$ 
B)  576$\pi$ 
C)  288$\pi$ 
D)  432$\pi$

Question 15

Solve the problem.
-Set up the triple integral for the volume of the sphere   in cylindrical coordinates.

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)  2$\pi$ 
B)    $\pi$ 
C)    $\pi$ 
D)  4$\pi$ 
A)  2$\pi$ 
B)    $\pi$ 
C)    $\pi$ 
D)  4$\pi$

Question 18

Provide an appropriate response.
-What form do planes perpendicular to the z-axis have in spherical coordinates?

Accepted Answer

A)    = a sin   
B)    = a sec   
C)    = a csc   
D)    = a cos   
A)    = a sin   
B)    = a sec   
C)    = a csc   
D)    = a cos

Question 19

Find the volume of the indicated region.
-the tetrahedron cut off from the first octant by the plane

Accepted Answer

A)  120 
B)  80 
C)  40 
D)  60 
A)  120 
B)  80 
C)  40 
D)  60

Question 20

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

Accepted Answer

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

Change the Cartesian integral to an equivalent polar integral, and then evaluate. -

Change the order of integration and evaluate the integral. -

Solve the problem. -Find the center of mass of the hemisphere of constant density bounded and the

Find the volume of the indicated region. -the region that lies under the plane and above the square

Evaluate the spherical coordinate integral. -

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

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

Solve the problem. -Let D be the region that is bounded below by the cone and above by the sphere Set up the triple integral for the volume of D in spherical coordinates.

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

Evaluate the integral. -

Evaluate the cylindrical coordinate integral. -

Change the Cartesian integral to an equivalent polar integral, and then evaluate. -

Find the volume of the indicated region. -the region bounded by the cylinder and the planes and

Use cylindrical coordinates to find the volume of the indicated region. -the region bounded by the cylinders and the planes

Solve the problem. -Set up the triple integral for the volume of the sphere in cylindrical coordinates.

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

Change the order of integration and evaluate the integral. -

Provide an appropriate response. -What form do planes perpendicular to the z-axis have in spherical coordinates?

Find the volume of the indicated region. -the tetrahedron cut off from the first octant by the plane

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

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Exam 16: Multiple Integration

Change the Cartesian integral to an equivalent polar integral, and then evaluate. -

Change the order of integration and evaluate the integral. -

Solve the problem. -Find the center of mass of the hemisphere of constant density bounded and the

Find the volume of the indicated region. -the region that lies under the plane and above the square

Evaluate the spherical coordinate integral. -

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

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

Solve the problem. -Let D be the region that is bounded below by the cone and above by the sphere Set up the triple integral for the volume of D in spherical coordinates.

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

Evaluate the integral. -

Evaluate the cylindrical coordinate integral. -

Change the Cartesian integral to an equivalent polar integral, and then evaluate. -

Find the volume of the indicated region. -the region bounded by the cylinder and the planes and

Use cylindrical coordinates to find the volume of the indicated region. -the region bounded by the cylinders and the planes

Solve the problem. -Set up the triple integral for the volume of the sphere in cylindrical coordinates.

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

Change the order of integration and evaluate the integral. -

Provide an appropriate response. -What form do planes perpendicular to the z-axis have in spherical coordinates?

Find the volume of the indicated region. -the tetrahedron cut off from the first octant by the plane

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

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