Explanation Given : Function y = x 4 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 = x 4 , its first derivation with respect to x is : d y d x = d d x ( x 4 ) = 4 x 3 &...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 48E

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The surface area of revolution about x axis of the function $y = x^{4}$ over the interval $[0, 1]$ .

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Chapter 9.2, Problem 47E

Chapter 9.2, Problem 49E

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The surface area of revolution about x axis of the function y = x 4 over the interval [ 0 , 1 ] .

Solution Summary: The author explains that the required surface area is approximately 3.43653 square units that is obtained when the function y = x 4 is rotated along a given interval.

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The surface area of revolution about x axis of the function $y = x^{4}$ over the interval $[0, 1]$ .

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Chapter 9 Solutions

The surface area of revolution about x axis of the function y = x 4 over the interval [ 0 , 1 ] .

Solution Summary: The author explains that the required surface area is approximately 3.43653 square units that is obtained when the function y = x 4 is rotated along a given interval.

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The surface area of revolution about x axis of the function y=x4 over the interval [0,1].

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Chapter 9 Solutions

The surface area of revolution about x axis of the function $y = x^{4}$ over the interval $[0, 1]$ .