Question 1

True or False. The centroid of a triangle with vertices (0, 0), (6, 9), and (6, -9) is (2, 0).

Accepted Answer

A) True 
 B)False

Question 2

Find the arc length of the curve  from x = 1 to x = 3.

Accepted Answer

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

Question 3

Assume 84 J of work stretch a spring 4 cm. Find the spring constant in J/cm.

Accepted Answer

The answer of Assume 84 J of work stretch a...

Question 4

Find the volume of the solid generated when the region enclosed by  , y = 4, and x = 0 is revolved about the y-axis.

Accepted Answer

The answer of Find the volume of the solid generated...

Question 5

Find the area of the region enclosed by y = x² - 6x + 6 and y = x.

Accepted Answer

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

Question 6

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft³.)

Accepted Answer

The answer of What is the force exerted by water...

Question 7

Evaluate sinh(7).

Accepted Answer

A)  0.6570 
B)  1.5221 
C)  548.3161 
D)  0.1433 
E)  49

Question 8

Answer true or false. The curves  , y = x3 / 27 intersect at x = 0 and x = 3

Accepted Answer

A) True 
 B)False

Question 9

True or False. The mass of the lamina enclosed by the x-axis, the graph of y = x2, and x = 1 with a density  = 5 is given by the integral:

Accepted Answer

A) True 
 B)False

Question 10

Answer true or false. The curves y = sin 3x, y = x5 intersect at x = 0 and x =  $\pi$.

Accepted Answer

A) True 
 B)False

Question 11

Use a graphing utility to find the area enclosed by the curves x = y3, x = y, y = 2, and y = 6. Approximate area to two decimal places.

Accepted Answer

A)  306 
B)  2 
C)  304 
D)  66 
E)  1

Question 12

Approximate the arc length of y = sin x from x = 0 to  .

Accepted Answer

A)  0.747 
B)  0.347 
C)  0.747 $\pi$ 
D)  0.547 
E)  0.547 $\pi$

Question 13

Find the fluid pressure on the top of a rectangular plate submerged in water at a depth of 2 m. (The weight density of water is $\rho$ = 9,810 N/m³.)

Accepted Answer

The answer of Find the fluid pressure on the top...

Question 14

Answer true or false. A semicircular wall 8 ft across the top forms one vertical end of a tank. The total force exerted on this wall by water, if the tank is full of water, is 12,546.26 lb. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

A) True 
 B)False

Question 15

Find f'(x) if f(x) = (sinh ^- ¹x)^x .

Accepted Answer

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

Question 16

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = (7 - x)², x = 7, and y = 1 is revolved about the line x = 7.

Accepted Answer

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

Question 17

Find the volume of the solid that results when the area of the region enclosed by x + y = 4, y = 0, x = 0 is revolved about the y axis

Accepted Answer

The answer of Find the volume of the solid that...

Question 18

Use cylindrical shells to find the volume of the solid when the region enclosed by y = sin(x2), y = 0, x = 0, x = 0.9 is revolved about the y-axis.

Accepted Answer

A)  0.689 $\pi$ 
B)  0.211 $\pi$ 
C)  0.311 $\pi$ 
D)  0.622 $\pi$ 
E)  0.378 $\pi$

Question 19

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves x = 10 - 5y2, x = 0, y = 0, x = 5 about the y-axis. Approximate area to three decimal places.

Accepted Answer

A)  111.072 
B)  78.540 
C)  11.806 
D)  236.954 
E)  90.346

Question 20

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between  and y = x is revolved about the y-axis.

Accepted Answer

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

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

True or False. The centroid of a triangle with vertices (0, 0), (6, 9), and (6, -9) is (2, 0).

Find the arc length of the curve from x = 1 to x = 3.

Assume 84 J of work stretch a spring 4 cm. Find the spring constant in J/cm.

Find the volume of the solid generated when the region enclosed by , y = 4, and x = 0 is revolved about the y-axis.

Find the area of the region enclosed by y = x² - 6x + 6 and y = x.

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft³.)

Evaluate sinh(7) .

Answer true or false. The curves , y = x³ / 27 intersect at x = 0 and x = 3

True or False. The mass of the lamina enclosed by the x-axis, the graph of y = x², and x = 1 with a density = 5 is given by the integral:

Answer true or false. The curves y = sin 3x, y = x⁵ intersect at x = 0 and x = $\pi$ .

Use a graphing utility to find the area enclosed by the curves x = y³, x = y, y = 2, and y = 6. Approximate area to two decimal places.

Approximate the arc length of y = sin x from x = 0 to $Approximate the arc length of y = sin x from x = 0 to . A) 0.747 B) 0.347 C) 0.747 \pi D) 0.547 E) 0.547 \pi$ .

Find the fluid pressure on the top of a rectangular plate submerged in water at a depth of 2 m. (The weight density of water is $\rho$ = 9,810 N/m³.)

Answer true or false. A semicircular wall 8 ft across the top forms one vertical end of a tank. The total force exerted on this wall by water, if the tank is full of water, is 12,546.26 lb. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Find f'(x) if f(x) = (sinh ^- ¹x)^x .

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = (7 - x)², x = 7, and y = 1 is revolved about the line x = 7.

Find the volume of the solid that results when the area of the region enclosed by x + y = 4, y = 0, x = 0 is revolved about the y axis

Use cylindrical shells to find the volume of the solid when the region enclosed by y = sin(x²) , y = 0, x = 0, x = 0.9 is revolved about the y-axis.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves x = 10 - 5y², x = 0, y = 0, x = 5 about the y-axis. Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between and y = x is revolved about the y-axis.

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

True or False. The centroid of a triangle with vertices (0, 0), (6, 9), and (6, -9) is (2, 0).

Find the arc length of the curve from x = 1 to x = 3.

Assume 84 J of work stretch a spring 4 cm. Find the spring constant in J/cm.

Find the volume of the solid generated when the region enclosed by , y = 4, and x = 0 is revolved about the y-axis.

Find the area of the region enclosed by y = x2 - 6x + 6 and y = x.

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft3.)

Evaluate sinh(7) .

Answer true or false. The curves , y = x3 / 27 intersect at x = 0 and x = 3

True or False. The mass of the lamina enclosed by the x-axis, the graph of y = x2, and x = 1 with a density = 5 is given by the integral:

Answer true or false. The curves y = sin 3x, y = x5 intersect at x = 0 and x = π\piπ .

Use a graphing utility to find the area enclosed by the curves x = y3, x = y, y = 2, and y = 6. Approximate area to two decimal places.

Approximate the arc length of y = sin x from x = 0 to .

Find the fluid pressure on the top of a rectangular plate submerged in water at a depth of 2 m. (The weight density of water is ρ\rhoρ = 9,810 N/m3.)

Answer true or false. A semicircular wall 8 ft across the top forms one vertical end of a tank. The total force exerted on this wall by water, if the tank is full of water, is 12,546.26 lb. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

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

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = (7 - x)2 , x = 7, and y = 1 is revolved about the line x = 7.

Find the volume of the solid that results when the area of the region enclosed by x + y = 4, y = 0, x = 0 is revolved about the y axis

Use cylindrical shells to find the volume of the solid when the region enclosed by y = sin(x2) , y = 0, x = 0, x = 0.9 is revolved about the y-axis.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves x = 10 - 5y2, x = 0, y = 0, x = 5 about the y-axis. Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between and y = x is revolved about the y-axis.

Find the area of the region enclosed by y = x² - 6x + 6 and y = x.

What is the force exerted by water on a surface of a square, vertical plate with edges of 3 ft if it is suspended with its top 3 ft below the surface? (The density of water is 62.4 lb/ft³.)

Answer true or false. The curves , y = x³ / 27 intersect at x = 0 and x = 3

True or False. The mass of the lamina enclosed by the x-axis, the graph of y = x², and x = 1 with a density = 5 is given by the integral:

Answer true or false. The curves y = sin 3x, y = x⁵ intersect at x = 0 and x = $\pi$ .

Use a graphing utility to find the area enclosed by the curves x = y³, x = y, y = 2, and y = 6. Approximate area to two decimal places.

Approximate the arc length of y = sin x from x = 0 to $Approximate the arc length of y = sin x from x = 0 to . A) 0.747 B) 0.347 C) 0.747 \pi D) 0.547 E) 0.547 \pi$ .

Find the fluid pressure on the top of a rectangular plate submerged in water at a depth of 2 m. (The weight density of water is $\rho$ = 9,810 N/m³.)

Answer true or false. A semicircular wall 8 ft across the top forms one vertical end of a tank. The total force exerted on this wall by water, if the tank is full of water, is 12,546.26 lb. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Find f'(x) if f(x) = (sinh ^- ¹x)^x .

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = (7 - x)², x = 7, and y = 1 is revolved about the line x = 7.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = sin(x²) , y = 0, x = 0, x = 0.9 is revolved about the y-axis.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves x = 10 - 5y², x = 0, y = 0, x = 5 about the y-axis. Approximate area to three decimal places.