Explanation Given information: The line of equation x = 1 in the region ℜ 3 about AB . The radius r 1 = 1 − y 4 and r 2 = 1 − y . The region lies between a = 0 and b = 1 . Calculation: To find the area of the region as shown below. A ( y ) = π r 1 2 − π r 2 2 = π × ( 1 − y 4 ) 2 − π ( 1 − y ) 2 = π ( ( 1 + y 8 − 2 y 4 ) − ( 1 + y 2 − 2 y ) ) = π ( y 8 − 2 y 4 − y 2 + 2 y ) The expression to find the volume generated by rotating the region ℜ 3 about AB as shown below. V = ∫ a b A ( y ) d y (1) Substitute 0 for a , 1 for b and π ( y 8 − 2 y 4 − y 2 + 2 y ) for A ( y ) in Equation (1)

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

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Chapter 6.2, Problem 29E

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To calculate: The volume generated by rotating the region about the line AB.

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Chapter 6.2, Problem 28E

Chapter 6.2, Problem 30E

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Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The volume generated by rotating the region about the line AB .

Solution Summary: The author calculates the volume generated by rotating the region about the line AB.

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Chapter 6 Solutions