Explanation Given information: The given function is y = x 3 and the interval is [ 0 , 10 ] . Formula used: Assume that f ( x ) ≥ 0 and f ′ exists and continuous on the interval [ a , b ] . The surface area S of revolution about the x -axis over the interval is given by S = 2 π ∫ a b f ( x ) 1 + [ f ′ ( x ) ] 2 d x The power rule of indefinite integrals. ∫ x n d x = x n n + 1 + C Calculation: Consider the given function. y = f ( x ) = x 3 Differentiate the above function with respect to x . f ′ ( x ) = 3 x 2 The given interval is [ 0 , 10 ] . Here, a = 0 , b = 10 For 0 ≤ x ≤ 10 , x ≥ 0 and f ′ exists and continuous on [ 0 , 10 ] . Now calculate the surface area of revolution about x -axis over the interval [ 0 , 10 ] as shown below

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

21st Edition

ISBN: 9781319438333

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8.2, Problem 40E

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Thesurface area of revolution about the x -axis over the interval [0,10] for the given function.

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Chapter 8.2, Problem 39E

Chapter 8.2, Problem 41E

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Chapter 8 Solutions

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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Thesurface area of revolution about the x -axis over the interval [ 0 , 10 ] for the given function.

Solution Summary: The author explains how to compute the surface area of revolution about the x -axis over the interval.

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To compute:

Thesurface area of revolution about the x -axis over the interval [0,10] for the given function.

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Chapter 8 Solutions

Thesurface area of revolution about the x -axis over the interval [ 0 , 10 ] for the given function.

Solution Summary: The author explains how to compute the surface area of revolution about the x -axis over the interval.

Videos

To compute: Thesurface area of revolution about the x -axis over the interval [0,10] for the given function.

Want to see the full answer?

Chapter 8 Solutions

To compute:

Thesurface area of revolution about the x -axis over the interval [0,10] for the given function.