Explanation Given info: ∫ c y 2 d x − x 2 d y y = x 2 y = x 0 ≤ x ≤ 1 Formula used: ∮ ∂ D p d x + Q d x = ∬ D ∂ Q ∂ x − ∂ p ∂ y d A Calculation: P = y 2 , Q = x 2 ∫ c y 2 d x − x 2 d y = ∯ D ∂ ∂ x ( x 2 ) − ∂ ∂ y ( y 2 ) d A ∫ c y 2 d x − x 2 d y = ∫ 0 1 ∫ x 2 x [ 2 x − 2 y ] d y d x ∫ c y 2 d x − x 2 d y = ∫ 0 1 ∫ x 2 x [ 2 ( x − y ) ] d y d x ∫ c y 2 d x − x 2 d y =

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 5CRE

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To evaluate the line integral $\int_{c} y^{2} d x - x^{2} d y$

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Chapter 18, Problem 4CRE

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Chapter 18 Solutions

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