Explanation Given information: The arc of the curve is f ( x ) = 1 3 x 3 + 1 4 x − 1 on [ 1 , 2 ] . 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 ) = 1 3 x 3 + 1 4 x − 1 on [ 1 , 2 ] Differentiating with respect to ‘x’, we get f ' ( x ) = 1 3 ( 3 x 2 ) + 1 4 ( − x − 2 ) = x 2 − 1 4 x 2 = 4 x 4 − 1 4 x 2 f ' is continuous on the interval on. [ 1 , 2 ] Then the surface area generated by revolving about x-axis the arc of the curve f ( x ) = 1 3 x 3 + 1 4 x − 1 on [ 1 , 2 ] is given by s = 2 π ∫ 1 2 ( 1 3 x 3 + 1 4 x − 1 ) 1 + [ 4 x

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.4, Problem 27PS

To determine

To find:The surface area generated by revolving about the x-axis the arc of the curve f(x)=13x3+14x−1 on [1,2] .

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Chapter 6.4, Problem 26PS

Chapter 6.4, Problem 28PS

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 ) = 1 3 x 3 + 1 4 x − 1 on [ 1 , 2 ] .

Solution Summary: The author calculates that the surface area generated by revolving about x-axis the arc of the curve is 25.28 unit square.

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To find:The surface area generated by revolving about the x-axis the arc of the curve f(x)=13x3+14x−1 on [1,2] .

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Chapter 6 Solutions