Explanation Given : Function y = x 2 and interval [ 0 , 4 ] 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 = x 2 , its first derivation with respect to x is : d y d x = d d x ( x 2 ) = 2 x ( ∵ d d x x n = n x n − 1 ) Thus, d s = 1 + ( 2 x ) 2 d x = 1 + 4 x 2 d x So required area is calculated as : A = ∫ 0 4 2 π x 2 ( 1 + 4 x 2 d x ) ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 40E

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Compute the surface area of revolution about x axis of the function $y = x^{2}$ over the interval $[0, 4]$ .

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Chapter 9.2, Problem 39E

Chapter 9.2, Problem 41E

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Compute the surface area of revolution about x axis of the function y = x 2 over the interval [ 0 , 4 ] .

Solution Summary: The author explains how to calculate the surface area of revolution of a function y = x 2 over the interval [ 0, 4 ].

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Compute the surface area of revolution about x axis of the function $y = x^{2}$ over the interval $[0, 4]$ .

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Chapter 9 Solutions

Compute the surface area of revolution about x axis of the function y = x 2 over the interval [ 0 , 4 ] .

Solution Summary: The author explains how to calculate the surface area of revolution of a function y = x 2 over the interval [ 0, 4 ].

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Compute the surface area of revolution about x axis of the function y=x2 over the interval [0,4].

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Chapter 9 Solutions

Compute the surface area of revolution about x axis of the function $y = x^{2}$ over the interval $[0, 4]$ .