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: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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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 4E (HC) W/ ACHIEVE ACCESS

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

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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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.