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

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.1, Problem 35E

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

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Chapter 9.1, Problem 34E

Chapter 9.1, Problem 36E

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

Solution Summary: The author explains that the required surface area is 16 2 square units when the function y = x graph under interval [ 0, 4 ] is rotated along X axis.

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

Solution Summary: The author explains that the required surface area is 16 2 square units when the function y = x graph under interval [ 0, 4 ] is rotated along X axis.

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

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Chapter 9 Solutions

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