Explanation Given : Function y = x − 1 and interval [ 1 , 3 ] 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 − 1 , its first derivation with respect to x is : d y d x = d d x ( x − 1 ) = − x − 1 − 1 ( ∵ d d x x n = n x n − 1 ) = − 1 x 2 Thus, d s = 1 + ( − 1 x 2 ) 2 d x = 1 + x 4 x 4 d x = 1 x 2 1 + x 4 d x Thus, using above formula for calculating area required, it changes as, A = ∫ 1 3 2 π ( 1 x ) 1 x 2 1 + x 4 d x &...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 47E

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The surface area of revolution about x axis of the function $y = x^{- 1}$ over the interval $[1, 3]$ .

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Chapter 9.2, Problem 46E

Chapter 9.2, Problem 48E

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The surface area of revolution about x axis of the function y = x − 1 over the interval [ 1 , 3 ] .

Solution Summary: The author explains how to determine the surface area of revolution about x axis of a function.

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The surface area of revolution about x axis of the function $y = x^{- 1}$ over the interval $[1, 3]$ .

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Chapter 9 Solutions

The surface area of revolution about x axis of the function y = x − 1 over the interval [ 1 , 3 ] .

Solution Summary: The author explains how to determine the surface area of revolution about x axis of a function.

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The surface area of revolution about x axis of the function y=x−1 over the interval [1,3].

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Chapter 9 Solutions

The surface area of revolution about x axis of the function $y = x^{- 1}$ over the interval $[1, 3]$ .