Explanation Given : Function y = e − x and interval [ 0 , 1 ] as well as revolution of this function about x axis. There is a prebuilt formula to calculate the total surface area of revolution when the graph of a function, in a given interval is rotated along x axis and for that we need the differentiation of this function with respect to x also, so that its value can be put in said formula, to get the required surface area. Formula to be used : Required surface area A is calculated using the formula, A = ∫ a b 2 π y d s Where d s is calculated using the formula, d s = 1 + ( d y d x ) 2 d x And ‘ a ’ be the lower limit of the given interval and ‘ b ’ be the upper limit of that interval. Calculation : Here for the given function y = e − x , its first derivation with respect to x is : d y d x = d d x ( e − x ) = e − x d d x ( − x ) ( ∵ d d x e x = e x ) = − e − x Thus, d s = 1 + ( − e − x ) 2 d x = 1 + e − 2 x d x So required area is calculated as : A = ∫ 0 1 2 π e − x ( 1 + e − 2 x d x ) ( ∵ y = e − x ) = 2 π ∫ 0 1 e − x ( 1 + e − 2 x d x ) ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 44E

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Compute the surface area of revolution about x axis of the function $y = e^{- x}$ over the interval $[0, 1]$ .

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Chapter 9.2, Problem 43E

Chapter 9.2, Problem 45E

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Compute the surface area of revolution about x axis of the function y = e − x over the interval [ 0 , 1 ] .

Solution Summary: The author explains how to calculate the surface area of revolution about x axis of the function y = e .

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Compute the surface area of revolution about x axis of the function $y = e^{- x}$ over the interval $[0, 1]$ .

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Chapter 9 Solutions

Compute the surface area of revolution about x axis of the function y = e − x over the interval [ 0 , 1 ] .

Solution Summary: The author explains how to calculate the surface area of revolution about x axis of the function y = e .

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Compute the surface area of revolution about x axis of the function y=e−x over the interval [0,1].

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Chapter 9 Solutions

Compute the surface area of revolution about x axis of the function $y = e^{- x}$ over the interval $[0, 1]$ .