Explanation Given: The function is y = 2 e − x . Formula used: Surface area of a differentiable function is given by, S = ∫ a b y 1 + ( y ′ ) 2 d x Calculation: Consider the expression y = 2 e − x . Differentiate y to get, y ′ = − 2 e − x Surface area of a differentiable function is given by, S = 2 π ∫ a b y 1 + ( y ′ ) 2 d x Then, surface area over the interval [ 0 , ∞ ) is given by, S = 2 π ∫ 0 ∞ 2 e − x 1 + ( − 2 e − x ) 2 d x = 4 π ∫ 0 ∞ e − x 1 + 4 e − 2 x d x Substitute e − x = u , d u = − e − x d x to get, ∫ e − x 1 + 4 e − 2 x d x = − ∫ 1 + 4 u 2 d u = − 1 4 [ 2 u 4 u 2 + 1 + ln | 2 u + 4 u 2 + 1 | ] + C = − 1 4 [ 2 e − x 4 ( e − x ) 2 + 1 + ln | 2 e − x + 4 ( e

7th Edition

ISBN: 9781337553032

Author: Larson, Ron, Edwards, Bruce H.

Publisher: Cengage Learning,

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Chapter 8.8, Problem 70E

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To calculate: Area of the surface formed revolving the graph of the given function y=2e−x on interval [0,∞) about the x−axis.

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Chapter 8.8, Problem 69E

Chapter 8.8, Problem 71E

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Chapter 8 Solutions

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Area of the surface formed revolving the graph of the given function y = 2 e − x on interval [ 0 , ∞ ) about the x − axis .

Solution Summary: The author calculates the surface area of a differentiable function y=2e-x on the x-axis.

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To calculate: Area of the surface formed revolving the graph of the given function y=2e−x on interval [0,∞) about the x−axis.

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Chapter 8 Solutions