Explanation Given information: The graph of the equation x 2 3 + y 2 3 = 1 is an asteroid. 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: The length of the entire curve is four times the length of the arc in the first quadrant. y = ( 1 − x 2 3 ) 3 2 on [ 0 , 1 ] (Given) Differentiating y = ( 1 − x 2 3 ) 3 2 with respect to ‘x’, we get f ' ( x ) = 3 2 ( 1 − x 2 3 ) 3 2 − 1 ( 2 3 x 2 3 − 1 ) = x − 1 3 ( 1 − x 2 3 ) 1 2 ⇒ [ f ' ( x ) ] 2 = ( x − 1 3 ( 1 − x 2 3 ) 1 2 ) 2 ⇒ [ f ' ( x ) ] 2 = x − 2 3 ( 1 − x 2 3 ) ⇒ [ f ' ( x

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.4, Problem 49PS

To determine

To find:The length of the asteroid by finding the length of the first quadrant portion, y=(1−x 2 3 )32 on [0,1] .

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Chapter 6.4, Problem 48PS

Chapter 6.4, Problem 50PS

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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The length of the asteroid by finding the length of the first quadrant portion, y = ( 1 − x 2 3 ) 3 2 on [ 0 , 1 ] .

Solution Summary: The author calculates the length of the asteroid by finding its length in the first quadrant.

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To find:The length of the asteroid by finding the length of the first quadrant portion, y=(1−x 2 3 )32 on [0,1] .

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Chapter 6 Solutions