Explanation Given information: The arc of the curve is f ( x ) = x on [ 2 , 6 ] . Formula used: If f ' is continuous on the interval [ a , b ] , then the surface generated by revolving about x-axis the arc of the curve y = f ( x ) on [ a , b ] has surface area s = 2 π ∫ a b f ( x ) 1 + [ f ' ( x ) ] 2 d x Calculation: f ( x ) = x on [ 2 , 6 ] Differentiating with respect to ‘x’, we get f ' ( x ) = 1 2 x f ' is continuous on the interval on [ 2 , 6 ] . Then the surface area generated by revolving about x-axis the arc of the curve f ( x ) = x on [ 2 , 6 ] is given by s = 2 π ∫ 2 6 f ( x ) 1 + [ f ' ( x ) ] 2 d x = 2 π ∫ 2 6 x 1 +</

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.4, Problem 25PS

To determine

To find:The surface area generated by revolving about the x-axis the arc of the curve f(x)=x on [2,6] .

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Chapter 6.4, Problem 24PS

Chapter 6.4, Problem 26PS

Chapter 6 Solutions

Calculus

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The surface area generated by revolving about the x-axis the arc of the curve f ( x ) = x on [ 2 , 6 ] .

Solution Summary: The author explains how the surface area generated by revolving about x-axis the arc of the curve f(x)=sqrtx is given.

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To find:The surface area generated by revolving about the x-axis the arc of the curve f(x)=x on [2,6] .

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Chapter 6 Solutions