Question 1

Find the length of the curve.
-y =   , 2 $\le$ x $\le$ 5

Accepted Answer

A)  21 
B)  6 
C)  14 
D)  21/2 
A)  21 
B)  6 
C)  14 
D)  21/2

Question 2

Solve the problem.   
-A swimming pool has the shape of a box with a base that measures 29 m by 15 m and a depth of 3 m. How much work is required to pump the water out of the pool when it is full?

Accepted Answer

A)  1,957,500 J 
B)  19,183,500 J 
C)  38,367,000 J 
D)  72,765,000 J 
A)  1,957,500 J 
B)  19,183,500 J 
C)  38,367,000 J 
D)  72,765,000 J

Question 3

Find the area of the shaded region.          
-

Accepted Answer

A)  4 +   
B)  4 
C)  8 
D)    
A)  4 +   
B)  4 
C)  8 
D)

Question 4

Find the area of the surface generated when the given curve is revolved about the x-axis.
-y =   on

Accepted Answer

A)  1132/49  $\pi$ 
B)  263/9 $\pi$ 
C)  4528 $\pi$ 
D)  15, 551/ 756  $\pi$ 
A)  1132/49  $\pi$ 
B)  263/9 $\pi$ 
C)  4528 $\pi$ 
D)  15, 551/ 756  $\pi$

Question 5

Find the volume of the described solid. 
-The base of the solid is the disk   +   $\le$ 9. The cross sections by planes perpendicular to the   between   and   are isosceles right triangles with one leg in the disk.

Accepted Answer

A)  144 
B)  90 
C)  18 
D)  72 
A)  144 
B)  90 
C)  18 
D)  72

Question 6

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
-y = 8   , y = 0, x = 1

Accepted Answer

A)  16$\pi$ 
B)  40$\pi$ 
C)  16/5 $\pi$ 
D)  32/5$\pi$ 
A)  16$\pi$ 
B)  40$\pi$ 
C)  16/5 $\pi$ 
D)  32/5$\pi$

Question 7

Set up an integral for the length of the curve.
-x = sin 5y, -  $\pi$ $\le$ y $\le$ 0

Accepted Answer

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

Question 8

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
-y = 4   , y = 0, x = 0, x = 1

Accepted Answer

A)  4   $\pi$ 
B)  8   $\pi$ 
C)  4(e - 1) $\pi$ 
D)  8   $\pi$ 
A)  4   $\pi$ 
B)  8   $\pi$ 
C)  4(e - 1) $\pi$ 
D)  8   $\pi$

Question 9

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. 
-About the x-axis y = 5 
X = 5

Accepted Answer

A)  250/3  $\pi$ 
B)  125/6  $\pi$ 
C)  125 /3  $\pi$ 
D)  125  $\pi$ 
A)  250/3  $\pi$ 
B)  125/6  $\pi$ 
C)  125 /3  $\pi$ 
D)  125  $\pi$

Question 10

Find the area enclosed by the given curves.
-y = 2x - x2, y = 2x - 4

Accepted Answer

A)  37/3 
B)  32/3 
C)  34/3 
D)  31/3 
A)  37/3 
B)  32/3 
C)  34/3 
D)  31/3

Question 11

Find the area enclosed by the given curves.
-Find the area of the region between the curve y =   and the interval 0 $\le$ x $\le$2 on the x-axis.

Accepted Answer

A)  24/ ln 5 
B)  25 
C)  25 / In 5 
D)  24 In 5 
A)  24/ ln 5 
B)  25 
C)  25 / In 5 
D)  24 In 5

Question 12

Find the area of the surface generated when the given curve is revolved about the y-axis.  
-y =   , for   $\le$ x $\le$ 9

Accepted Answer

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

Question 13

Solve the problem.   
-The following figure shows the shape and dimensions of a small dam. Assuming the water level is at the top of the dam, find the total force on the face of the dam.

Accepted Answer

A)  17,860,500 N 
B)  89,302,500 N 
C)  396,900 N 
D)  9,922,500 N 
A)  17,860,500 N 
B)  89,302,500 N 
C)  396,900 N 
D)  9,922,500 N

Question 14

Find the area enclosed by the given curves.
-y = - 4sin x, y = sin 2x, 0 $\le$ x $\le$ $\pi$

Accepted Answer

A)  1/2 
B)  8 
C)  16 
D)  4 
A)  1/2 
B)  8 
C)  16 
D)  4

Question 15

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis.
-y =   , y = 0, y = x - 6

Accepted Answer

A)  27$\pi$ 
B)  63/4$\pi$ 
C)  225/2 $\pi$ 
D)  63/2 $\pi$ 
A)  27$\pi$ 
B)  63/4$\pi$ 
C)  225/2 $\pi$ 
D)  63/2 $\pi$

Question 16

Find the area of the surface generated when the given curve is revolved about the y-axis.  
-y =   , for 4 $\le$x$\le$ 6

Accepted Answer

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

Question 17

Use a calculator to approximate the area of the surface generated when the given curve is revolved about the x-axis. Round to two decimal places when necessary.
-y =   on [0, 1]

Accepted Answer

A)  0.13 
B)  1.35 
C)  0.38 
D)  3.28 
A)  0.13 
B)  1.35 
C)  0.38 
D)  3.28

Question 18

Write the integral that gives the surface area generated when the curve is revolved about the x-axis. Do not simplify.   
-y =   on [ 1, 4]

Accepted Answer

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

Question 19

Find the area enclosed by the given curves.
-Find the area of the "triangular" region in the first quadrant that is bounded above by the curve   , below by the curve y =   , and on the right by the line x = ln 2.

Accepted Answer

A)  1/2 
B)  0 
C)  11/2 
D)  2 ln 2 
A)  1/2 
B)  0 
C)  11/2 
D)  2 ln 2

Question 20

Find the area of the surface generated when the given curve is revolved about the x-axis.
-y = 2x + 5 on [0, 2]

Accepted Answer

A)    
B)  24    $\pi$ 
C)  28 $\pi$ 
D)  28   $\pi$ 
A)    
B)  24    $\pi$ 
C)  28 $\pi$ 
D)  28   $\pi$

Find the length of the curve. -y = $Find the length of the curve. -y = , 2 \le x \le 5$ , 2 $\le$ x $\le$ 5

Solve the problem. -A swimming pool has the shape of a box with a base that measures 29 m by 15 m and a depth of 3 m. How much work is required to pump the water out of the pool when it is full?

Find the area of the shaded region. -

Find the area of the surface generated when the given curve is revolved about the x-axis. -y = on

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. -y = 8 , y = 0, x = 1

Set up an integral for the length of the curve. -x = sin 5y, - $\pi$ $\le$ y $\le$ 0

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. -y = 4 , y = 0, x = 0, x = 1

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the x-axis y = 5 X = 5

Find the area enclosed by the given curves. -y = 2x - x², y = 2x - 4

Find the area enclosed by the given curves. -Find the area of the region between the curve y = $Find the area enclosed by the given curves. -Find the area of the region between the curve y = and the interval 0 \le x \le 2 on the x-axis.$ and the interval 0 $\le$ x $\le$ 2 on the x-axis.

Solve the problem. -The following figure shows the shape and dimensions of a small dam. Assuming the water level is at the top of the dam, find the total force on the face of the dam.

Find the area enclosed by the given curves. -y = - 4sin x, y = sin 2x, 0 $\le$ x $\le$ $\pi$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. -y = , y = 0, y = x - 6

Find the area of the surface generated when the given curve is revolved about the y-axis. -y = $Find the area of the surface generated when the given curve is revolved about the y-axis. -y = , for 4 \le x \le 6$ , for 4 $\le$ x $\le$ 6

Use a calculator to approximate the area of the surface generated when the given curve is revolved about the x-axis. Round to two decimal places when necessary. -y = on [0, 1]

Write the integral that gives the surface area generated when the curve is revolved about the x-axis. Do not simplify. -y = on [ 1, 4]

Find the area enclosed by the given curves. -Find the area of the "triangular" region in the first quadrant that is bounded above by the curve , below by the curve y = , and on the right by the line x = ln 2.

Find the area of the surface generated when the given curve is revolved about the x-axis. -y = 2x + 5 on [0, 2]

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Exam 6: Applications of Integration

Find the length of the curve. -y = , 2 ≤\le≤ x ≤\le≤ 5