Explanation Given information: The arc of the curve is f ( x ) = 2 3 x 3 2 on [ 0 , 3 ] . Formula used: If f ' is continuous on the interval [ a , b ] , then the surface generated by revolving about y-axis the arc of the curve y = f ( x ) on [ a , b ] has surface area s = 2 π ∫ a b x 1 + [ f ' ( x ) ] 2 d x Calculation: f ( x ) = 2 3 x 3 2 on [ 0 , 3 ] Differentiating with respect to ‘x’, we get f ' ( x ) = x 1 2 f ' is continuous on the interval on [ 0 , 3 ]

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 46PS

To determine

To find:The surface area generated by revolving about the y-axis the arc of the curve f(x)=23x32 on [0,3] .

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Chapter 6.4, Problem 45PS

Chapter 6.4, Problem 47PS

Chapter 6 Solutions

Calculus

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The surface area generated by revolving about the y-axis the arc of the curve f ( x ) = 2 3 x 3 2 on [ 0 , 3 ] .

Solution Summary: The author calculates that the surface area generated by revolving about y-axis the arc of the curve is 48.59 unit square.

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To find:The surface area generated by revolving about the y-axis the arc of the curve f(x)=23x32 on [0,3] .

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Chapter 6 Solutions