Question 1

Evaluate the integral.
-

Accepted Answer

A)  23.2 
B)  7 
C)  8 
D)  9

Question 2

Evaluate the double integral over the given region.
- R = {(x, y): 0 $\le$x$\le$1, 0$\le$y$\le$2}

Accepted Answer

A)   
B)   
C)  -  
D)

Question 3

Find the area of the region specified in polar coordinates.
-the region inside both  and

Accepted Answer

A)  16($\pi$ - 1) 
B)  8($\pi$ - 2) 
C)  8($\pi$ - 1) 
D)  16($\pi$ - 2)

Question 4

Evaluate the integral.
-

Accepted Answer

A)  27 
B)  9 
C)   
D)

Question 5

Solve the problem.
-Find the center of mass of the region of density  bounded by the paraboloid  and the xy-plane.

Accepted Answer

A)  
B)  
C)  
D)

Question 6

Find the volume of the indicated region.
-the region bounded by the coordinate planes, the parabolic cylinder  , and the plane

Accepted Answer

A)  6000 
B)  3000 
C)   
D)  8000

Question 7

Evaluate the double integral over the given region.
- R =

Accepted Answer

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

Question 8

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

Accepted Answer

A)  16 
B)  4 
C)  32 
D)  8

Question 9

Change the order of integration and evaluate the integral.
-

Accepted Answer

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

Question 10

Find the area of the region specified in polar coordinates.
-the region enclosed by the curve r = 5 + cos $\theta$

Accepted Answer

A)  13 $\pi$ 
B)  17 $\pi$ 
C)  26 $\pi$ 
D)    $\pi$

Question 11

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

Accepted Answer

A)   
B)   
C)   
D)

Question 12

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

Accepted Answer

A)    = a csc $\theta$ csc  
B)   = a csc $\theta$ 
C)    = a sin  sin $\theta$ 
D)   = a csc $\theta$

Question 13

Find the Jacobian for the given transformation
-

Accepted Answer

A)  -100 
B)  2400 
C)  -24 
D)  100

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

A)  4  - 68 
B)   -  
C)   - 1 
D)

Question 16

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

Accepted Answer

A)  -  
B)  - 45 
C)  -  
D)  - 405

Question 17

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

Accepted Answer

A)   
B)   
C)   
D)

Question 18

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)

Question 19

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

Accepted Answer

A)  160  64 -  ln 4097 
B)  320  64 -  ln 4097 
C)  160  64 - 5 ln 4097 
D)  320  64 - 5 ln 4097

Question 20

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

Accepted Answer

A)  36 
B)  324 
C)  2592 
D)  288

Exam 16: Multiple Integration

Evaluate the integral. -

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = {(x, y) : 0 \le x \le 1, 0 \le y \le 2} A) B) C) - D)$ R = {(x, y) : 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 2}

Evaluate the integral. -

Solve the problem. -Find the center of mass of the region of density bounded by the paraboloid and the xy-plane.

Find the volume of the indicated region. -the region bounded by the coordinate planes, the parabolic cylinder , and the plane

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = A) B) C) D) \pi$ R = $Evaluate the double integral over the given region. - R = A) B) C) D) \pi$

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

Change the order of integration and evaluate the integral. - $Change the order of integration and evaluate the integral. - A) \pi B) C) \pi D) \pi$

Find the area of the region specified in polar coordinates. -the region enclosed by the curve r = 5 + cos $\theta$

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

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

Find the Jacobian for the given transformation -

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

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

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

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

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

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

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

Exam 16: Multiple Integration

Evaluate the integral. -

Evaluate the double integral over the given region. - R = {(x, y) : 0 ≤\le≤ x ≤\le≤ 1, 0 ≤\le≤ y ≤\le≤ 2}

Find the area of the region specified in polar coordinates. -the region inside both and

Evaluate the integral. -

Solve the problem. -Find the center of mass of the region of density bounded by the paraboloid and the xy-plane.

Find the volume of the indicated region. -the region bounded by the coordinate planes, the parabolic cylinder , and the plane

Evaluate the double integral over the given region. - R =

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

Change the order of integration and evaluate the integral. -

Find the area of the region specified in polar coordinates. -the region enclosed by the curve r = 5 + cos θ\thetaθ

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

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

Find the Jacobian for the given transformation -

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

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

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

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

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

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

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

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = {(x, y) : 0 \le x \le 1, 0 \le y \le 2} A) B) C) - D)$ R = {(x, y) : 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 2}

Evaluate the double integral over the given region. - $Evaluate the double integral over the given region. - R = A) B) C) D) \pi$ R = $Evaluate the double integral over the given region. - R = A) B) C) D) \pi$

Change the order of integration and evaluate the integral. - $Change the order of integration and evaluate the integral. - A) \pi B) C) \pi D) \pi$

Find the area of the region specified in polar coordinates. -the region enclosed by the curve r = 5 + cos $\theta$

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