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

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ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8.2, Problem 44E

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Thesurface area of revolution about the x -axis over the interval [0,1] for the given function.

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Chapter 8.2, Problem 43E

Chapter 8.2, Problem 45E

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Chapter 8 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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Thesurface area of revolution about the x -axis over the interval [ 0 , 1 ] 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 [0,1] for the given function.

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Chapter 8 Solutions

Thesurface area of revolution about the x -axis over the interval [ 0 , 1 ] 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 [0,1] for the given function.

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Chapter 8 Solutions

To compute:

Thesurface area of revolution about the x -axis over the interval [0,1] for the given function.