Explanation Given information: Let n be a positive integer and C, D be constants such that n ( n − 1 ) = 1 16 C D 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: y = C x 2 n + D x 2 ( 1 − n ) (Given) Let f ( x ) = C x 2 n + D x 2 ( 1 − n ) Differentiating with respect to ‘x’, we get f ' ( x ) = C ( 2 n x 2 n − 1 ) + D ( 2 ( 1 − n ) x 2 ( 1 − n ) − 1 ) [ f ' ( x ) ] 2 = ( 2 C n x 2 n − 1 + 2 D ( 1 − n ) x 1 − 2 n ) 2 = ( 2 C n x 2 n − 1 + 2 D ( 1 − n ) 1 x 2 n − 1 ) 2 = ( 2 C n x 2 ( 2 n − 1 ) − 2 D ( n − 1 ) x 2 n − 1 ) 2 = ( 4 C 2 n 2 x 4 ( 2 n − 1 ) + 4 D 2 ( n − 1 ) 2 − 8 C D n ( n − 1 ) x 2 ( 2 n − 1 ) x 2 ( 2 n − 1 ) ) = ( 4 C 2 n 2 x 4 ( 2 n − 1 ) + 4 D 2 ( n − 1 ) 2 − 8 C D 1 16 C D x 2 ( 2 n − 1 ) x 2 ( 2 n − 1 ) ) = ( 4 C 2 n 2 x 4 ( 2 n − 1 ) + 4 D 2 ( 1 − n ) 2 − 1 2 x 2 ( 2 n − 1 ) x 2 ( 2 n − 1 ) ) The length of the arc of the curve y = C x 2 n + D x 2 ( 1 − n ) on [ a , b ] is given by s = ∫ a b 1 + [ f ' ( x ) ] 2 d x s = ∫ a b 1 + ( 4 C 2 n 2 x 4 ( 2 n − 1 ) + 4 D 2 ( n − 1 ) 2 − 1 2 x 2 ( 2 n − 1 ) x 2 ( 2 n − 1 ) ) d x = ∫</

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 57PS

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To find:The length of the curve y=Cx2n+Dx2(1−n) from x=a to x=b .

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Chapter 6.4, Problem 56PS

Chapter 6.4, Problem 58PS

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Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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The length of the curve y = C x 2 n + D x 2 ( 1 − n ) from x = a to x = b .

Solution Summary: The author calculates the length of the curve y=Cx2n+D

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To find:The length of the curve y=Cx2n+Dx2(1−n) from x=a to x=b .

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Chapter 6 Solutions