Explanation Given : Function y = 4 x + 3 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 = 4 x + 3 , its first derivation with respect to x is : d y d x = d d x ( 4 x + 3 ) = 4 d d x x + d d x 3 = 4 + 0 = 4 ( ∵ d d x c = 0 where c is constant ) Thus, d s = 1 + 4 2 d x = 17 d x So required area is calculated as : A = ∫ 0 1 2 π ( 4 x + 3 ) ( 17 d x )

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 38E

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To determine: The surface area of revolution about x axis of the function $y = 4 x + 3$ over the interval $[0, 1]$ .

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Chapter 9.2, Problem 37E

Chapter 9.2, Problem 39E

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T he surface area of revolution about x axis of the function y = 4 x + 3 over the interval [ 0 , 1 ] .

Solution Summary: The author explains the formula to calculate the required surface area of revolution when the graph of a function is rotated along x axis.

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To determine: The surface area of revolution about x axis of the function $y = 4 x + 3$ over the interval $[0, 1]$ .

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Chapter 9 Solutions

T he surface area of revolution about x axis of the function y = 4 x + 3 over the interval [ 0 , 1 ] .

Solution Summary: The author explains the formula to calculate the required surface area of revolution when the graph of a function is rotated along x axis.

Concept explainers

Videos

To determine: The surface area of revolution about x axis of the function y=4x+3 over the interval [0,1].

Want to see the full answer?

Chapter 9 Solutions

To determine: The surface area of revolution about x axis of the function $y = 4 x + 3$ over the interval $[0, 1]$ .