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

Find the area of the region enclosed by y = x2 - 3x and y = 9x - x2. Approximate area to three decimal places.

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

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

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 24, x + y = 10 is revolved about the y-axis.

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Question 1

Correct Answer:

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Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = , x = 3, and y = 0 is revolved about the line y = 9.

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Question 2

Correct Answer:

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= = =

True or False. The area of the region enclosed by the x-axis, the graph of y = x³, and x = 3 is given by the integral:

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(True/False)

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Question 3

Correct Answer:

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True

An object in deep space is initially considered to be stationary. If a force of 390 N acts on the object over a distance of 250 m, how much work is done on the object?

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Question 4

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y² = x⁷, x = 1, and y = 0 is revolved about the y-axis.

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Question 5

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

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Question 6

Answer true or false. The curves y = x⁴ + 2 and y = 3x + 2 intersect at x = 1 and x = 2.

(True/False)

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Question 7

Answer true or false. The area of the surface that is generated by revolving the portion of the curve y = x⁸ between x = 1 and x = 4 about the y-axis is .

(True/False)

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Question 8

Use cylindrical shells to find the volume of the solid when the region enclosed by and y = 0 between x = 1 and x = 4 is revolved about the y-axis.

(Multiple Choice)

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Question 9

Find f '(x) if .

(Short Answer)

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Question 10

Answer true or false. The arc length of y = x sin x from x = 0 to x = $\pi$ can be approximated to be 4.698.

(True/False)

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Question 11

Use cylindrical shells to find the volume of the solid generated when the region R under over the interval [0, 7] is revolved about the x-axis.

(Multiple Choice)

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Question 12

Answer true or false. The area of the surface generated by revolving the curve x = sin y, about the y-axis to be 5.83.

(True/False)

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Question 13

Find the area of the region enclosed by y = x² - 3x and y = 9x - x². Approximate area to three decimal places.

(Essay)

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Question 14

Find the area of the region enclosed by y = x³ + 3, x = -1, x = 2, and the x axis.

(Essay)

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Question 15

Write a definite integral to represent the area of the region enclosed by x² + y² = 8² , y = x, and x = 0. Do not evaluate.

(Essay)

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Question 16

A spring exerts a force of 5 N when stretched 10 cm. How much work, in Joules, is required to stretch the spring from a length of 30 cm from its natural length to a length of 70 cm from its natural length.?

(Essay)

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Question 17

Answer true or false. The volume of the solid that results when the region enclosed by the curves y = x⁴, y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

(True/False)

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Question 18

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = 9x, x = 16, and y = 0 is revolved about the y axis.

(Essay)

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Question 19

Find the arc length of the curve y = sin x over the interval x = 0 to x = 8 $\pi$ . Approximate area to four decimal places. Use a CAS if necessary.

(Essay)

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Question 20

Showing 1 - 20 of 314

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 24, x + y = 10 is revolved about the y-axis.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = , x = 3, and y = 0 is revolved about the line y = 9.

True or False. The area of the region enclosed by the x-axis, the graph of y = x³, and x = 3 is given by the integral:

An object in deep space is initially considered to be stationary. If a force of 390 N acts on the object over a distance of 250 m, how much work is done on the object?

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y² = x⁷, x = 1, and y = 0 is revolved about the y-axis.

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

Answer true or false. The curves y = x⁴ + 2 and y = 3x + 2 intersect at x = 1 and x = 2.

Answer true or false. The area of the surface that is generated by revolving the portion of the curve y = x⁸ between x = 1 and x = 4 about the y-axis is .

Use cylindrical shells to find the volume of the solid when the region enclosed by and y = 0 between x = 1 and x = 4 is revolved about the y-axis.

Find f '(x) if .

Answer true or false. The arc length of y = x sin x from x = 0 to x = $\pi$ can be approximated to be 4.698.

Use cylindrical shells to find the volume of the solid generated when the region R under over the interval [0, 7] is revolved about the x-axis.

Answer true or false. The area of the surface generated by revolving the curve x = sin y, about the y-axis to be 5.83.

Find the area of the region enclosed by y = x² - 3x and y = 9x - x². Approximate area to three decimal places.

Find the area of the region enclosed by y = x³ + 3, x = -1, x = 2, and the x axis.

Write a definite integral to represent the area of the region enclosed by x² + y² = 8² , y = x, and x = 0. Do not evaluate.

A spring exerts a force of 5 N when stretched 10 cm. How much work, in Joules, is required to stretch the spring from a length of 30 cm from its natural length to a length of 70 cm from its natural length.?

Answer true or false. The volume of the solid that results when the region enclosed by the curves y = x⁴, y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = 9x, x = 16, and y = 0 is revolved about the y axis.

Find the arc length of the curve y = sin x over the interval x = 0 to x = 8 $\pi$ . Approximate area to four decimal places. Use a CAS if necessary.

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

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

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 24, x + y = 10 is revolved about the y-axis.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = , x = 3, and y = 0 is revolved about the line y = 9.

True or False. The area of the region enclosed by the x-axis, the graph of y = x3, and x = 3 is given by the integral:

An object in deep space is initially considered to be stationary. If a force of 390 N acts on the object over a distance of 250 m, how much work is done on the object?

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y2 = x7, x = 1, and y = 0 is revolved about the y-axis.

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

Answer true or false. The curves y = x4 + 2 and y = 3x + 2 intersect at x = 1 and x = 2.

Answer true or false. The area of the surface that is generated by revolving the portion of the curve y = x8 between x = 1 and x = 4 about the y-axis is .

Use cylindrical shells to find the volume of the solid when the region enclosed by and y = 0 between x = 1 and x = 4 is revolved about the y-axis.

Find f '(x) if .

Answer true or false. The arc length of y = x sin x from x = 0 to x = π\piπ can be approximated to be 4.698.

Use cylindrical shells to find the volume of the solid generated when the region R under over the interval [0, 7] is revolved about the x-axis.

Answer true or false. The area of the surface generated by revolving the curve x = sin y, about the y-axis to be 5.83.

Find the area of the region enclosed by y = x2 - 3x and y = 9x - x2. Approximate area to three decimal places.

Find the area of the region enclosed by y = x3 + 3, x = -1, x = 2, and the x axis.

Write a definite integral to represent the area of the region enclosed by x2 + y2 = 82 , y = x, and x = 0. Do not evaluate.

A spring exerts a force of 5 N when stretched 10 cm. How much work, in Joules, is required to stretch the spring from a length of 30 cm from its natural length to a length of 70 cm from its natural length.?

Answer true or false. The volume of the solid that results when the region enclosed by the curves y = x4, y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y2 = 9x, x = 16, and y = 0 is revolved about the y axis.

Find the arc length of the curve y = sin x over the interval x = 0 to x = 8 π\piπ . Approximate area to four decimal places. Use a CAS if necessary.

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

True or False. The area of the region enclosed by the x-axis, the graph of y = x³, and x = 3 is given by the integral:

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y² = x⁷, x = 1, and y = 0 is revolved about the y-axis.

Answer true or false. The curves y = x⁴ + 2 and y = 3x + 2 intersect at x = 1 and x = 2.

Answer true or false. The area of the surface that is generated by revolving the portion of the curve y = x⁸ between x = 1 and x = 4 about the y-axis is .

Answer true or false. The arc length of y = x sin x from x = 0 to x = $\pi$ can be approximated to be 4.698.

Find the area of the region enclosed by y = x² - 3x and y = 9x - x². Approximate area to three decimal places.

Find the area of the region enclosed by y = x³ + 3, x = -1, x = 2, and the x axis.

Write a definite integral to represent the area of the region enclosed by x² + y² = 8² , y = x, and x = 0. Do not evaluate.

Answer true or false. The volume of the solid that results when the region enclosed by the curves y = x⁴, y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = 9x, x = 16, and y = 0 is revolved about the y axis.

Find the arc length of the curve y = sin x over the interval x = 0 to x = 8 $\pi$ . Approximate area to four decimal places. Use a CAS if necessary.