Explanation Given: y = 1 12 x 3 + x − 1 , x = 1 & x = 2 Key Concept and Formula Used: The arc length s of function y = f ( x ) over [ a , b ] is equal to s = ∫ a b 1 + ( f ' ( x ) ) 2 d x d d x x n = n x n − 1 , ∫ 1 x d x = ln x + C and ∫ x n d x = x n + 1 n + 1 + C Calculation: To calculate the arc length we first differentiate the given function and then use the formula to find the arc length. y = 1 12 x 3 + x − 1 = f ( x ) f ' ( x ) = d d x ( 1 12 x 3 + x − 1 ) = 1 12 × 3 x 2 + ( − 1 ) x − 1 − 1 f ' ( x ) = x 2 4 − x − 2 Arc length= s = ∫ a b 1 + ( f ' ( x ) ) 2 d x where a = 1 & b = 2 1 + ( f ' ( x ) )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 9.1, Problem 3E

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the arc length as an integral.

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Chapter 9.1, Problem 2E

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the arc length as an integral.

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