Explanation Given information: The curve is f ( x ) = 1 6 x 3 + 1 2 x − 1 on [ 1 , 2 ] . 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 6 x 3 + 1 2 x − 1 on [ 1 , 2 ] (Given) Differentiating f ( x ) = 1 6 x 3 + 1 2 x − 1 with respect to ‘x’, we get f ' ( x ) = 1 6 ( 3 x 2 ) + 1 2 ( − x − 2 ) = 1 2 ( x 2 ) − 1 2 ( x − 2 ) = ( x 2 2 ) − 1 2 x 2 = x 4 − 1 2 x 2 ⇒ [ f ' ( x ) ] 2 = ( x 4 − 1 2 x 2 ) 2 The length of the arc of the curve f ( x ) = 1 6 x 3 + 1 2 x − 1 on [ 1 , 2 ] is given by s = ∫ 1 2 1 + [ f ' ( x ) ] 2 d x = ∫ 1 2 1 + ( x 4 − 1 2 x 2

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 16PS

To determine

To find:The length of the arc of the curve f(x)=16x3+12x−1 on [1,2] .

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Chapter 6.4, Problem 15PS

Chapter 6.4, Problem 17PS

Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY

The length of the arc of the curve f ( x ) = 1 6 x 3 + 1 2 x − 1 on [ 1 , 2 ] .

Solution Summary: The formula used to find the length of the arc of a curve is f(x)=16x3+

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To find:The length of the arc of the curve f(x)=16x3+12x−1 on [1,2] .

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Chapter 6 Solutions