Explanation Given information: The curve is ( y + 1 ) 2 = 4 x 3 between the points ( 0 , − 1 ) and ( 1 , 1 ) . 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 equation of the curve ( y + 1 ) 2 = 4 x 3 is defined between the points ( 0 , − 1 ) and ( 1 , 1 ) . (Given) ( y + 1 ) 2 = 4 x 3 ⇒ ( y + 1 ) = 2 x 3 2 ⇒ y = 2 x 3 2 − 1 Differentiating f ( x ) = 2 x 3 2 − 1 with respect to ‘x’, we get f ' ( 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 20PS

To determine

To find:The length of the arc of the curve defined by (y+1)2=4x3 between the points (0,−1) and (1,1) .

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Chapter 6.4, Problem 19PS

Chapter 6.4, Problem 21PS

Chapter 6 Solutions

Calculus

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The length of the arc of the curve defined by ( y + 1 ) 2 = 4 x 3 between the points ( 0 , − 1 ) and ( 1 , 1 ) .

Solution Summary: The length of the curve defined by (y+1)2=4x3 is 4.67 units.

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To find:The length of the arc of the curve defined by (y+1)2=4x3 between the points (0,−1) and (1,1) .

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Chapter 6 Solutions