Explanation Given information: The given function is f ( x ) = x and the interval is [ 0 , 4 ] . 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 y -axis over the interval is given by S = 2 π ∫ a b x 1 + [ f ′ ( x ) ] 2 d x The following indefinite integral can be calculated as shown below. ∫ x 2 − a 2 d x = 1 2 x x 2 − a 2 − 1 2 ln | x + x 2 − a 2 | + C Calculation: Consider the given function. y = f ( x ) = x Differentiate the above function with respect to x . f ′ ( x ) = 1 2 x The given interval is [ 0 , 4 ] . Here, a = 0 , b = 4 For 0 ≤ x ≤ 4 , x ≥ 0 and f ′ exists and continuous on [ 0 , 4 ] . Now calculate the surface area of revolution about y -axis over the interval [ 0 , 4 ] as shown below

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 8.2, Problem 56E

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Thesurface area of revolution about the y -axis over the interval [0,4] for the given function.

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Chapter 8.2, Problem 55E

Chapter 8.2, Problem 57E

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Thesurface area of revolution about the y -axis over the interval [ 0 , 4 ] for the given function.

Solution Summary: The author calculates the surface area of revolution about the y -axis over the interval.

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To compute:

Thesurface area of revolution about the y -axis over the interval [0,4] for the given function.

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Chapter 8 Solutions

Thesurface area of revolution about the y -axis over the interval [ 0 , 4 ] for the given function.

Solution Summary: The author calculates the surface area of revolution about the y -axis over the interval.

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To compute: Thesurface area of revolution about the y -axis over the interval [0,4] for the given function.

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Chapter 8 Solutions

To compute:

Thesurface area of revolution about the y -axis over the interval [0,4] for the given function.