Explanation Given information: The given integral is ∫ C y d y over y = x 3 for 0 ≤ x ≤ 3 . Concept Used: The line integral over the curve C is given by ∫ C f ⋅ d r = ∫ a b f ( r ( t ) ) ⋅ ‖ r ' ( t ) ‖ d t where r ( t ) is the parametrization of the given curve C. Calculation: As given ∫ C x d x , first we parameterize the given curve which is y = x 3 . Let x = t ⇒ y = t 3 , 0 ≤ t ≤ 3 r ( t ) = 〈 t , t 3 〉 ⇒ r ' ( t ) = 〈 1 , 3 t 2 〉 Thus, f ( t , t 3 ) = t 3 ‖ r ' ( t ) ‖ = ( 1 ) 2 + ( 3 t 2 ) 2 = 1 + 9 t 4 Thus, ∫ C f ⋅ d r = ∫ a b f ( r ( t ) ) ⋅ ‖ r ' ( t ) ‖ d t

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 28E

To determine

To find: The line integral ∫Cydy over y=x3 for 0≤x≤3 .

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Chapter 17.2, Problem 27E

Chapter 17.2, Problem 29E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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The line integral ∫ C y d y over y = x 3 for 0 ≤ x ≤ 3 .

Solution Summary: The author explains how the line integral over the curve C is given by displaystyle

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To find: The line integral ∫Cydy over y=x3 for 0≤x≤3 .

Want to see the full answer?

Chapter 17 Solutions