Explanation Given : Function y = e − x 2 2 and interval [ 0 , 2 ] 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 2 2 , its first derivation with respect to x is : d y d x = d d x ( e − x 2 2 ) = e − x 2 2 d d x ( − x 2 2 ) ( ∵ d d x x n = n x n − 1 , d d x e x =

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 8.2, Problem 49E

To determine

The surface area of revolution about x axis of the function $y = e^{- \frac{x^{2}}{2}}$ over the interval $[0, 2]$ .

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Chapter 8.2, Problem 48E

Chapter 8.2, Problem 50E

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Chapter 8 Solutions

Calculus: Early Transcendentals

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Knowledge Booster

The surface area of revolution about x axis of the function y = e − x 2 2 over the interval [ 0 , 2 ] .

The surface area of revolution about x axis of the function y=e−x22 over the interval [0,2].

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Chapter 8 Solutions

The surface area of revolution about x axis of the function $y = e^{- \frac{x^{2}}{2}}$ over the interval $[0, 2]$ .