Question 1

Find the area of the surface generated by revolving x = 5y, 0 $\le$  y $\le$  1 about the y-axis. Approximate area to three decimal places.

Accepted Answer

A)  51.709 
B)  160.190422 
C)  103.418 
D)  11.452 
E)  80.095

Question 2

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

Accepted Answer

The answer of A swimming pool is 35 feet long...

Question 3

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

Accepted Answer

The answer of Use a graphing utility to find the...

Question 4

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x =  $\pi$.

Accepted Answer

A)  118.418 
B)  10.882 
C)  21.764 
D)  5.441 
E)  10.682

Question 5

Find the centroid of the region enclosed by the graphs of  , x = y , and y = 4.

Accepted Answer

The answer of Find the centroid of the region enclosed...

Question 6

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

A)  13,728 lb 
B)  68,640 lb 
C)  302,016 lb 
D)  24,200 lb 
E)  34,320 lb

Question 7

Use a graphing utility to find the area enclosed by the curves y = x3, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Accepted Answer

A)  56 
B)  2 
C)  54 
D)  17.33 
E)  1

Question 8

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x2, y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Accepted Answer

A)  17.772 
B)  12.566 
C)  1.889 
D)  37.913 
E)  14.455

Question 9

Find the area of the surface generated by revolving y = 3x, 0 $\le$  x $\le$  1 about the x-axis. Approximate area to three decimal places.

Accepted Answer

A)  14.022 
B)  59.608 
C)  28.044 
D)  11.452 
E)  29.804

Question 10

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Accepted Answer

The answer of A cylindrical tank is to be filled...

Question 11

Find f '(x) if  .

Accepted Answer

The answer of Find f '(x) if  ....

Question 12

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

Accepted Answer

The answer of Use cylindrical shells to find the volume...

Question 13

Find the arc length of the curve  from y = 1 to y = 2.

Accepted Answer

The answer of Find the arc length of the curve...

Question 14

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

Accepted Answer

The answer of Use the method of disks to find...

Question 15

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

Accepted Answer

The answer of Find f '(x) if f(x) = sinh...

Question 16

Find the arc length of the curve  from y = 1 to y = 8.

Accepted Answer

The answer of Find the arc length of the curve...

Question 17

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

Accepted Answer

The answer of Find the work done when a constant...

Question 18

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

Accepted Answer

The answer of Find the area of the region enclosed...

Question 19

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

Accepted Answer

A) True 
 B)False

Question 20

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.

Accepted Answer

The answer of Use a graphing utility to find the...

Exam 6: Applications of the Definite Integral in Geometry, Science and Engineering

Find the area of the surface generated by revolving x = 5y, 0 $\le$ y $\le$ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = $\pi$ .

Find the centroid of the region enclosed by the graphs of , x = y , and y = 4.

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Use a graphing utility to find the area enclosed by the curves y = x³, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 $\le$ x $\le$ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Find f '(x) if .

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

Find the arc length of the curve from y = 1 to y = 2.

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

Find the arc length of the curve from y = 1 to y = 8.

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.

Exam 6: Applications of the Definite Integral in Geometry, Science and Engineering

Find the area of the surface generated by revolving x = 5y, 0 ≤\le≤ y ≤\le≤ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft3).

Use a graphing utility to find the area of the region enclosed by the curves x = y7, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = π\piπ .

Find the centroid of the region enclosed by the graphs of , x = y , and y = 4.

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Use a graphing utility to find the area enclosed by the curves y = x3, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x2, y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 ≤\le≤ x ≤\le≤ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft3. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Find f '(x) if .

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x2, y = 4, and x = 0 is revolved about the x-axis.

Find the arc length of the curve from y = 1 to y = 2.

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y2 = x3, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh - 1(sin 9x).

Find the arc length of the curve from y = 1 to y = 8.

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

Find the area of the region enclosed by x = y2 - 3 and x = 5-y2.

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

Use a graphing utility to find the area of the region enclosed by the curves y = x9, y = 0, x = -2, x = 2.

Find the area of the surface generated by revolving x = 5y, 0 $\le$ y $\le$ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = $\pi$ .

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Use a graphing utility to find the area enclosed by the curves y = x³, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 $\le$ x $\le$ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.