Explanation Given information: The function f ( x ) have a revolution about the x-axis for the given function and interval: f ( x ) = e − x , [ 0 , 10 ] Concept used: If f is continuous and f ( x ) ≥ 0 on [ a , b ] , then the solid obtained by rotating the region under the graph about the x-axis has the volume: V = π ∫ a b R 2 d x = π ∫ a b [ f ( x ) ] 2 d x Substitution method of integration : This formula is used to transform one integral into another integral and that integral will be easy to calculate. Calculation: Put the value of f ( x ) in given formula and solve the function: V = π ∫ a b [ f ( x ) ] 2 d x V = π ∫ 0 10 ( e − x ) 2 d x V = π ∫ 0 10 e − 2 x d x Assume that − 2 x = u . Differentiate with respect to “ x ”. We get: ⇒ d d x ( − 2 x ) d x = d d x ( u ) d u ⇒ − 2 d x = d u ⇒ d x = − 1 2 d u Substitute the value of x and d x

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 6.3, Problem 12E

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Calculate the volume of revolution about x -axis for the function f(x)=e−x and interval [0,10].

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Chapter 6.3, Problem 11E

Chapter 6.3, Problem 13E

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Chapter 6 Solutions

Calculus: Early Transcendentals

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Calculate the volume of revolution about x -axis for the function f ( x ) = e − x and interval [ 0 , 10 ] .

Solution Summary: The author calculates the volume of revolution about x-axis for the function f(x)=e-x and interval [0,10].

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Calculate the volume of revolution about x -axis for the function f(x)=e−x and interval [0,10].

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Chapter 6 Solutions