Question 1

Answer true or false.   =

Accepted Answer

A) True 
 B)False

Question 2

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x3 - 6x2 + 8x over [0, 2] is revolved about the y-axis.

Accepted Answer

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

Question 3

Masses m1 = 7, m2 = 9, m3 = 11 are positioned on a weightless on a weightless beam as shown in the figure.   Where should be fulcrum be placed so that the beam is in equilibrium?

Accepted Answer

A)    
B)    
C)    
D)  11 
E)    
A)    
B)    
C)    
D)  11 
E)

Question 4

The arc length of the curve   from y = 0 to y = 1 is

Accepted Answer

A)  3.333 
B)  1.166 
C)  1.197 
D)  3.491 
E)  1.132 
A)  3.333 
B)  1.166 
C)  1.197 
D)  3.491 
E)  1.132

Question 5

$\int$ sinh(7x + 8) dx =

Accepted Answer

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

Question 6

Find the volume of the solid generated when the region between the graphs   and   over the interval [0, 1] is revolved about the x-axis.

Accepted Answer

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

Question 7

Find the work done when a variable force of F(x) = 10x N in the positive x direction moves an object from x = 0 m to x = 4 m.

Accepted Answer

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

Question 8

Find the arc length of the curve y = 2x3/2 from x = 0 to x = 5. Approximate area to two decimal places.

Accepted Answer

A)  23.04 $\pi$ 
B)  310.99 
C)  310.99 $\pi$ 
D)  23.11 
E)  23.04 
A)  23.04 $\pi$ 
B)  310.99 
C)  310.99 $\pi$ 
D)  23.11 
E)  23.04

Question 9

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

Question 10

Answer true or false. Assume a spring is stretched 40 cm by a force of 34 N. The work needed to do this is 6.8 J.

Accepted Answer

A) True 
 B)False

Question 11

Answer true or false. It takes the same amount of work to move an object from 16,000 km above the earth to 96,000 km above the earth as it does to move the object from 289,000 km above the earth to 369,000 km above the earth.

Accepted Answer

A) True 
 B)False

Question 12

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = 2x, x = 0, and y = 6 is revolved about x = 3.

Accepted Answer

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

Question 13

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x2 - 5x, y = 0 is revolved about the y-axis.

Accepted Answer

A)    
B)  625 $\pi$ 
C)    
D)  6 $\pi$ 
E)    
A)    
B)  625 $\pi$ 
C)    
D)  6 $\pi$ 
E)

Question 14

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x2 and x = y2 is revolved about the y-axis.

Accepted Answer

Question 15

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x2, x = 2, x = 4, y = 0 is revolved about the line x = 2.

Accepted Answer

A)  45.333 $\pi$ 
B)  22.667 $\pi$ 
C)  330.667 $\pi$ 
D)  11.333 $\pi$ 
E)  2.011 $\pi$ 
A)  45.333 $\pi$ 
B)  22.667 $\pi$ 
C)  330.667 $\pi$ 
D)  11.333 $\pi$ 
E)  2.011 $\pi$

Question 16

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y2 = x3, x = 4, and y = 0 is revolved about the y axis.

Accepted Answer

Question 17

A trapezoidal gate in a dam that is 5 feet wide at the top, 3 feet wide at the bottom, and 4 feet tall is submerged in water (weight density 62.4 lbs/ft3) as shown in the figure. Find the force on the gate when the surface of the water is 2 feet above the top of the gate.

Accepted Answer

@#IMG-DLM& , @#IMG-DLM& , @#IMG-DLM& @#IMG-DLM& =

Question 18

Use cylindrical shells to find the volume of the solid that results when the region enclosed by xy = 8, x + y = 9 is revolved about the y-axis.

Accepted Answer

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

Question 19

Answer true or false. The area of the surface generated by revolving   , 5 $\le$ y $\le$7 about the y-axis is given by   .

Accepted Answer

A) True 
 B)False

Question 20

Approximate the area of the surface generated by revolving the curve y = sin x,   , about the x-axis. Approximate area to three decimal places.

Accepted Answer

A)  14.424 
B)  8.439 
C)  7.212 
D)  6.912 
E)  3.606 
A)  14.424 
B)  8.439 
C)  7.212 
D)  6.912 
E)  3.606

Answer true or false. =

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x³ - 6x² + 8x over [0, 2] is revolved about the y-axis.

Masses m₁ = 7, m₂ = 9, m₃ = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

The arc length of the curve from y = 0 to y = 1 is

$\int$ sinh(7x + 8) dx =

Find the volume of the solid generated when the region between the graphs and over the interval [0, 1] is revolved about the x-axis.

Find the work done when a variable force of F(x) = 10x N in the positive x direction moves an object from x = 0 m to x = 4 m.

Find the arc length of the curve y = 2x^3/2 from x = 0 to x = 5. Approximate area to two decimal places.

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Answer true or false. Assume a spring is stretched 40 cm by a force of 34 N. The work needed to do this is 6.8 J.

Answer true or false. It takes the same amount of work to move an object from 16,000 km above the earth to 96,000 km above the earth as it does to move the object from 289,000 km above the earth to 369,000 km above the earth.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = 2x, x = 0, and y = 6 is revolved about x = 3.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x² - 5x, y = 0 is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x² and x = y² is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x², x = 2, x = 4, y = 0 is revolved about the line x = 2.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 4, and y = 0 is revolved about the y axis.

A trapezoidal gate in a dam that is 5 feet wide at the top, 3 feet wide at the bottom, and 4 feet tall is submerged in water (weight density 62.4 lbs/ft³) as shown in the figure. Find the force on the gate when the surface of the water is 2 feet above the top of the gate.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by xy = 8, x + y = 9 is revolved about the y-axis.

Approximate the area of the surface generated by revolving the curve y = sin x, , about the x-axis. Approximate area to three decimal places.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

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

Answer true or false. =

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x3 - 6x2 + 8x over [0, 2] is revolved about the y-axis.

Masses m1 = 7, m2 = 9, m3 = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

The arc length of the curve from y = 0 to y = 1 is

∫\int∫ sinh(7x + 8) dx =

Find the volume of the solid generated when the region between the graphs and over the interval [0, 1] is revolved about the x-axis.

Find the work done when a variable force of F(x) = 10x N in the positive x direction moves an object from x = 0 m to x = 4 m.

Find the arc length of the curve y = 2x3/2 from x = 0 to x = 5. Approximate area to two decimal places.

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Answer true or false. Assume a spring is stretched 40 cm by a force of 34 N. The work needed to do this is 6.8 J.

Answer true or false. It takes the same amount of work to move an object from 16,000 km above the earth to 96,000 km above the earth as it does to move the object from 289,000 km above the earth to 369,000 km above the earth.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = 2x, x = 0, and y = 6 is revolved about x = 3.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x2 - 5x, y = 0 is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x2 and x = y2 is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x2, x = 2, x = 4, y = 0 is revolved about the line x = 2.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y2 = x3, x = 4, and y = 0 is revolved about the y axis.

A trapezoidal gate in a dam that is 5 feet wide at the top, 3 feet wide at the bottom, and 4 feet tall is submerged in water (weight density 62.4 lbs/ft3) as shown in the figure. Find the force on the gate when the surface of the water is 2 feet above the top of the gate.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by xy = 8, x + y = 9 is revolved about the y-axis.

Answer true or false. The area of the surface generated by revolving , 5 ≤\le≤ y ≤\le≤ 7 about the y-axis is given by .

Approximate the area of the surface generated by revolving the curve y = sin x, , about the x-axis. Approximate area to three decimal places.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x³ - 6x² + 8x over [0, 2] is revolved about the y-axis.

Masses m₁ = 7, m₂ = 9, m₃ = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

$\int$ sinh(7x + 8) dx =

Find the arc length of the curve y = 2x^3/2 from x = 0 to x = 5. Approximate area to two decimal places.

A semicircular wall 10 ft across the top forms one vertical end of a tank. What is the total force exerted on this wall by water if the tank is full of water? Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x² - 5x, y = 0 is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y = x² and x = y² is revolved about the y-axis.

Use cylindrical shells to find the volume of the solid when the region enclosed by y = x², x = 2, x = 4, y = 0 is revolved about the line x = 2.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 4, and y = 0 is revolved about the y axis.

A trapezoidal gate in a dam that is 5 feet wide at the top, 3 feet wide at the bottom, and 4 feet tall is submerged in water (weight density 62.4 lbs/ft³) as shown in the figure. Find the force on the gate when the surface of the water is 2 feet above the top of the gate.