Explanation Given: F ( x , y ) = e − y i − x e − y j Calculation: The given vector filed is F ( x , y ) = e − y i − x e − y j Here, u = e − y , v = − x e − y The condition for the vector filed F is conservative is given by ∂ u ∂ y = ∂ v ∂ x Now, find ∂ u ∂ y = ∂ ∂ y ( e − y ) = − e − y And ∂ v ∂ x = ∂ ∂ x ( − x e − y ) = − e − y Since, ∂ u ∂ y = ∂ v ∂ x hence, the vector filed is conservative. Let f ( x , y ) is a scalar function such that F = ∇ f So, we have f ( x , y ) = ∫ u d x = ∫ e − y d x = x e − y + g ( y ) Here, g ( y ) is the constant of integration

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ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 13.3, Problem 26PS

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To find: The scalar function f and show that the vector filed is conservative. Then find the line integral ∫CF⋅ dR where C is any smooth path connecting A(0,0) to B(1,1)

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The scalar function f and show that the vector filed is conservative. Then find the line integral ∫ C F ⋅ d R where C is any smooth path connecting A ( 0 , 0 ) to B ( 1 , 1 )

Solution Summary: The author explains how to find the scalar function f and show that the vector filed is conservative.

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To find: The scalar function f and show that the vector filed is conservative. Then find the line integral ∫CF⋅ dR where C is any smooth path connecting A(0,0) to B(1,1)

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Chapter 13 Solutions