Explanation Given information: The given integral is ∫ C y d x − x d y over y = x 2 for 0 ≤ x ≤ 2 . Concept Used: The line integral over the curve C is given by ∫ C P d x + Q d y = ∫ a b [ P ( x ( t ) , y ( t ) ) d x d t + Q ( x ( t ) , y ( t ) ) d y d t ] d t where r ( t ) = ( x ( t ) , y ( t ) ) is the parametrization of the given curve C. Calculation: As given ∫ C y d x − x d y , first we parameterize the given curve which is y = x 2 . Let x = t ⇒ y = t 2 , 0 ≤ t ≤ 2 Thus, ∫ C f ⋅ d r = ∫ a b [ P ( x ( t ) , y ( t )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 29E

To determine

To find: The line integral ∫Cydx−xdy over y=x2 for 0≤x≤2 .

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Chapter 17.2, Problem 28E

Chapter 17.2, Problem 30E

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The line integral ∫ C y d x − x d y over y = x 2 for 0 ≤ x ≤ 2 .

Solution Summary: The author explains that the line integral over the curve C is given by displaystyleundersetCint.

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To find: The line integral ∫Cydx−xdy over y=x2 for 0≤x≤2 .

Want to see the full answer?

Chapter 17 Solutions