Explanation Given information: The arc of the curve is f ( x ) = 1 3 ( 12 − x ) 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 ) = 1 3 ( 12 − x ) on [ 0 , 3 ] Differentiating with respect to ‘x’, we get f ' ( x ) = − 1 3 f ' is continuous on the interval on [ 0 , 3 ]

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 45PS

To determine

To find:The surface area generated by revolving about the y-axis the arc of the curve f(x)=13(12−x) on [0,3] .

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Chapter 6.4, Problem 44PS

Chapter 6.4, Problem 46PS

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Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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The surface area generated by revolving about the y-axis the arc of the curve f ( x ) = 1 3 ( 12 − x ) on [ 0 , 3 ] .

Solution Summary: The author calculates that the surface area generated by revolving about y-axis the arc of the curve is f(x)=13(12-x)

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To find:The surface area generated by revolving about the y-axis the arc of the curve f(x)=13(12−x) on [0,3] .

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Chapter 6 Solutions