Explanation Given information: The curve is f ( x ) = 1 3 ( 2 + x 2 ) 3 2 on [ 1 , 4 ] . Formula used: The length of the arc of the curve f ( x ) on [ a , b ] is given by s = ∫ a b 1 + [ f ' ( x ) ] 2 d x Calculation: f ( x ) = 1 3 ( 2 + x 2 ) 3 2 on [ 1 , 4 ] (Given) Differentiating f ( x ) = 1 3 ( 2 + x 2 ) 3 2 with respect to ‘x’, we get f ' ( x ) = 1 3 × 3 2 ( 2 + x 2 ) 3 2 − 1 ( 2 x ) = x ( 2 + x 2 ) 1 2 ⇒ [ f ' ( x ) ] 2 = ( x ( 2 + x 2 ) 1 2 ) 2 ⇒ [ f ' ( x ) ] 2 = x 2 ( 2 + x 2 )

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 8PS

To determine

To find:The length of the arc of the curve f(x)=13(2+x2)32 on [1,4] .

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Chapter 6.4, Problem 7PS

Chapter 6.4, Problem 9PS

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Chapter 6 Solutions

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The length of the arc of the curve f ( x ) = 1 3 ( 2 + x 2 ) 3 2 on [ 1 , 4 ] .

Solution Summary: The formula used to find the length of the arc of a curve is given by f(x)=13(2+x2)

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To find:The length of the arc of the curve f(x)=13(2+x2)32 on [1,4] .

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Chapter 6 Solutions