Explanation Given information: The region is enclosed by the functions y = sin − 1 x , x − axis , x = 1 . Formula used: The volume of the solid of rotation of the function f ( y ) about the x − axis from y = a to y = b is given by the formula, Volume = 2 π ∫ a b y f ( y ) d y Calculation: Consider that the region is bounded by the functions y = sin − 1 x , x − axis , x = 1 . First sketch the graph of the functions y = sin − 1 x , x − axis , x = 1 as given below: Now, observe from the graph that here f ( x ) = sin − 1 x and the limit of the integral is from x = 0 to x = 1 . Compute the corresponding limit of y and the function f ( y ) as given below, f ( x ) = sin − 1 x y = sin − 1 x At x = 0 , y = sin − 1 0 = 0 At x = 1 , y = sin − 1 1 = π 2 y = sin − 1 x y 2 = sin − 1 x x = sin y 2 The volume of the solid of rotation of the region enclosed about the x − axis is given by the formula, Volume = 2 π ∫ 0 π 2 y sin y 2 d y Compute the value of the integral

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 6.4, Problem 62E

To determine

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The volume of the solid generated by rotating the region enclosed by the graph, about the x−axis.

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Chapter 6.4, Problem 61E

Chapter 6.4, Problem 63E

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Chapter 6 Solutions

Calculus: Early Transcendentals

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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Tocalculate: The volume of the solid generated by rotating the region enclosed by the graph, about the x − axis .

Solution Summary: The author calculates the volume of the solid generated by rotating the region enclosed by the graph, about the x-axis.

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Tocalculate:

The volume of the solid generated by rotating the region enclosed by the graph, about the x−axis.

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Chapter 6 Solutions

Tocalculate: The volume of the solid generated by rotating the region enclosed by the graph, about the x − axis .

Solution Summary: The author calculates the volume of the solid generated by rotating the region enclosed by the graph, about the x-axis.

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Tocalculate: The volume of the solid generated by rotating the region enclosed by the graph, about the x−axis.

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Chapter 6 Solutions

Tocalculate:

The volume of the solid generated by rotating the region enclosed by the graph, about the x−axis.