Question 1

Change the order of integration and evaluate the integral.
-

Accepted Answer

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

Question 2

Change the order of integration and evaluate the integral.
-

Accepted Answer

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

Question 3

Use the given transformation to evaluate the integral.
-  where R is the parallelogram bounded by the lines

Accepted Answer

A)    
B)    
C)    
D)  585 
A)    
B)    
C)    
D)  585

Question 4

Use the given transformation to evaluate the integral.
- 
 where R is the parallelogram bounded by the lines

Accepted Answer

A)  3 
B)  -6 
C)  -3 
D)  6 
A)  3 
B)  -6 
C)  -3 
D)  6

Question 5

Use the given transformation to evaluate the integral.
-  where R is the parallelepiped bounded by the planes

Accepted Answer

A)    
B)  15,708 
C)  3927 
D)  35,343 
A)    
B)  15,708 
C)  3927 
D)  35,343

Question 6

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

Accepted Answer

A)  3(e - 1) 
B)    (e - 1) 
C)    (2e - 1) 
D)  3(2e - 1) 
A)  3(e - 1) 
B)    (e - 1) 
C)    (2e - 1) 
D)  3(2e - 1)

Question 7

Evaluate the double integral over the given region.
-  R = {(x, y): 9 $\le$x$\le$10, 9$\le$y$\le$10}

Accepted Answer

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

Question 8

Evaluate the spherical coordinate integral.
-

Accepted Answer

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

Question 9

Evaluate the cylindrical coordinate integral.
-

Accepted Answer

A)  12$\pi$ 
B)  6$\pi$ 
C)  96$\pi$ 
D)  48$\pi$ 
A)  12$\pi$ 
B)  6$\pi$ 
C)  96$\pi$ 
D)  48$\pi$

Question 10

Find the volume of the indicated region.
-the solid cut from the first octant by the surface

Accepted Answer

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

Question 11

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 12

Use cylindrical coordinates to find the volume of the indicated region.
-the region enclosed by the cylinder   and the planes   and

Accepted Answer

A)  125$\pi$ 
B)  250$\pi$ 
C)  500$\pi$ 
D)  375$\pi$ 
A)  125$\pi$ 
B)  250$\pi$ 
C)  500$\pi$ 
D)  375$\pi$

Question 13

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

Accepted Answer

A)  10 ln 2 ln cos 7 
B)  5 ln 2 ln cos 7 
C)  - 10 ln 2 ln cos 7 
D)  - 5 ln 2 ln cos 7 
A)  10 ln 2 ln cos 7 
B)  5 ln 2 ln cos 7 
C)  - 10 ln 2 ln cos 7 
D)  - 5 ln 2 ln cos 7

Question 14

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

Accepted Answer

A)  ln 8 - 1 
B)    
C)  ln 8 
D)    
A)  ln 8 - 1 
B)    
C)  ln 8 
D)

Question 15

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)  8$\pi$ 
B)  32$\pi$ 
C)  4$\pi$ 
D)  64$\pi$ 
A)  8$\pi$ 
B)  32$\pi$ 
C)  4$\pi$ 
D)  64$\pi$

Question 16

Change the order of integration and evaluate the integral.
-

Accepted Answer

A)      
B)      
C)  81   
D)  243   
A)      
B)      
C)  81   
D)  243

Question 17

Find the Jacobian for the given transformation
-x = 6u cos 5v, y = 6u sin 5v

Accepted Answer

A)  180u 
B)  150v 
C)  180v 
D)  150u 
A)  180u 
B)  150v 
C)  180v 
D)  150u

Question 18

Change the order of integration and evaluate the integral.
-

Accepted Answer

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

Question 19

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

Accepted Answer

A)    ln 344 
B)    ln 344 
C)    ln 2402 
D)    ln 2402 
A)    ln 344 
B)    ln 344 
C)    ln 2402 
D)    ln 2402

Question 20

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

Accepted Answer

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

Change the order of integration and evaluate the integral. -

Change the order of integration and evaluate the integral. -

Use the given transformation to evaluate the integral. - where R is the parallelogram bounded by the lines

Use the given transformation to evaluate the integral. - where R is the parallelogram bounded by the lines

Use the given transformation to evaluate the integral. - where R is the parallelepiped bounded by the planes

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

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = {(x, y): 9 \le x \le 10, 9 \le y \le 10}$ R = {(x, y): 9 $\le$ x $\le$ 10, 9 $\le$ y $\le$ 10}

Evaluate the spherical coordinate integral. -

Evaluate the cylindrical coordinate integral. -

Find the volume of the indicated region. -the solid cut from the first octant by the surface

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 .

Use cylindrical coordinates to find the volume of the indicated region. -the region enclosed by the cylinder and the planes and

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

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

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

Change the order of integration and evaluate the integral. -

Find the Jacobian for the given transformation -x = 6u cos 5v, y = 6u sin 5v

Change the order of integration and evaluate the integral. -

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

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

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Exam 16: Multiple Integration

Change the order of integration and evaluate the integral. -

Change the order of integration and evaluate the integral. -

Use the given transformation to evaluate the integral. - where R is the parallelogram bounded by the lines

Use the given transformation to evaluate the integral. - where R is the parallelogram bounded by the lines

Use the given transformation to evaluate the integral. - where R is the parallelepiped bounded by the planes

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

Evaluate the double integral over the given region. - R = {(x, y): 9 ≤\le≤ x ≤\le≤ 10, 9 ≤\le≤ y ≤\le≤ 10}

Evaluate the spherical coordinate integral. -

Evaluate the cylindrical coordinate integral. -

Find the volume of the indicated region. -the solid cut from the first octant by the surface

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 .

Use cylindrical coordinates to find the volume of the indicated region. -the region enclosed by the cylinder and the planes and

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

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

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

Change the order of integration and evaluate the integral. -

Find the Jacobian for the given transformation -x = 6u cos 5v, y = 6u sin 5v

Change the order of integration and evaluate the integral. -

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

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

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. - $Evaluate the double integral over the given region. - R = {(x, y): 9 \le x \le 10, 9 \le y \le 10}$ R = {(x, y): 9 $\le$ x $\le$ 10, 9 $\le$ y $\le$ 10}