Question 1

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

Accepted Answer

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

Question 2

Use cylindrical coordinates to find the volume of the indicated region.
-the region bounded below by the xy-plane, laterally by the cylinder   and above by the plane

Accepted Answer

A)  400$\pi$ 
B)  50$\pi$ 
C)  10$\pi$ 
D)  80$\pi$ 
A)  400$\pi$ 
B)  50$\pi$ 
C)  10$\pi$ 
D)  80$\pi$

Question 3

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

Accepted Answer

A)  49 
B)    
C)    
D)  98 
A)  49 
B)    
C)    
D)  98

Question 4

Find the center of mass of the thin rod with the given density function.
-Find the center of mass of a thin rod that lies along the semicircle y =   if the density of the rod is

Accepted Answer

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

Question 5

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

Accepted Answer

A)  5 sin 6 
B)  6 cos 5 
C)  6 sin 5 
D)  5 cos 6 
A)  5 sin 6 
B)  6 cos 5 
C)  6 sin 5 
D)  5 cos 6

Question 6

Find the center of mass of a thin plate of constant density covering the given region.
-The region enclosed by the parabolas y = -   + 18 and y =

Accepted Answer

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

Question 7

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.
-z = 4   + 9   ; R = {(x, y): 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1}

Accepted Answer

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

Question 8

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 9

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

Accepted Answer

A)    
B)    
C)  24 
D)  15 
A)    
B)    
C)  24 
D)  15

Question 10

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)

Question 11

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)    $\pi$(15 $\pi$ - 16) 
B)    $\pi$ (15$\pi$ - 8) 
C)    $\pi$ (15 $\pi$ - 8) 
D)    $\pi$ (15$\pi$ - 16) 
A)    $\pi$(15 $\pi$ - 16) 
B)    $\pi$ (15$\pi$ - 8) 
C)    $\pi$ (15 $\pi$ - 8) 
D)    $\pi$ (15$\pi$ - 16)

Question 12

Find the average value of the function f over the given region.
-f(x, y) = sin 3(x + y); R =

Accepted Answer

A)    
B)  4   
C)    
D)    
A)    
B)  4   
C)    
D)

Question 13

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

Accepted Answer

A)  - 3 
B)  2 
C)  13 
D)  3 
A)  - 3 
B)  2 
C)  13 
D)  3

Question 14

Find the center of mass of a thin plate covering the given region with the given density function.
-The region enclosed by the parabolas y = 72 -   and y =   , with density  (x) =

Accepted Answer

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

Question 15

Find the average value of over the given region.  
-  over the rectangular solid in the first octant bounded by the coordinate planes and the planes     ,   ,

Accepted Answer

A)    
B)  4 
C)  6 
D)  9 
A)    
B)  4 
C)  6 
D)  9

Question 16

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

Accepted Answer

A)    $\pi$ 
B)     $\pi$ 
C)     $\pi$ 
D)  56 $\pi$ 
A)    $\pi$ 
B)     $\pi$ 
C)     $\pi$ 
D)  56 $\pi$

Question 17

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

Accepted Answer

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

Question 18

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)    $\pi$ 
B)    $\pi$ 
C)  7$\pi$ 
D)  14$\pi$ 
A)    $\pi$ 
B)    $\pi$ 
C)  7$\pi$ 
D)  14$\pi$

Question 19

Find the average value of over the given region.  
-  +   over the rectangular solid in the first octant bounded by the coordinate planes and the planes       ,,

Accepted Answer

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

Question 20

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

Accepted Answer

A)  27 
B)  756 
C)  108 
D)  189 
A)  27 
B)  756 
C)  108 
D)  189

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

Use cylindrical coordinates to find the volume of the indicated region. -the region bounded below by the xy-plane, laterally by the cylinder and above by the plane

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

Find the center of mass of the thin rod with the given density function. -Find the center of mass of a thin rod that lies along the semicircle y = if the density of the rod is

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

Find the center of mass of a thin plate of constant density covering the given region. -The region enclosed by the parabolas y = - + 18 and y =

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

Choose the one alternative that best completes the statement or answers the question. 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 lines , , and

Change the order of integration and evaluate the integral. -

Find the average value of the function f over the given region. -f(x, y) = sin 3(x + y); R =

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

Find the center of mass of a thin plate covering the given region with the given density function. -The region enclosed by the parabolas y = 72 - and y = , with density (x) =

Find the average value of over the given region. - over the rectangular solid in the first octant bounded by the coordinate planes and the planes , ,

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

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

Change the order of integration and evaluate the integral. -

Find the average value of over the given region. - + over the rectangular solid in the first octant bounded by the coordinate planes and the planes ,,

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

Functions

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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

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Vector Calculus

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Exam 16: Multiple Integration

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

Use cylindrical coordinates to find the volume of the indicated region. -the region bounded below by the xy-plane, laterally by the cylinder and above by the plane

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

Find the center of mass of the thin rod with the given density function. -Find the center of mass of a thin rod that lies along the semicircle y = if the density of the rod is

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

Find the center of mass of a thin plate of constant density covering the given region. -The region enclosed by the parabolas y = - + 18 and y =

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries. -z = 4 + 9 ; R = {(x, y): 0 ≤\le≤ x ≤\le≤ 1, 0 ≤\le≤ y ≤\le≤ 1}

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

Choose the one alternative that best completes the statement or answers the question. 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 lines , , and

Change the order of integration and evaluate the integral. -

Find the average value of the function f over the given region. -f(x, y) = sin 3(x + y); R =

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

Find the center of mass of a thin plate covering the given region with the given density function. -The region enclosed by the parabolas y = 72 - and y = , with density (x) =

Find the average value of over the given region. - over the rectangular solid in the first octant bounded by the coordinate planes and the planes , ,

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

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

Change the order of integration and evaluate the integral. -

Find the average value of over the given region. - + over the rectangular solid in the first octant bounded by the coordinate planes and the planes ,,

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