Apostol page 386, problem 5(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Given [tex]f,g[/tex] continuously differentiable on open connected [tex]S[/tex] in the plane, show

[tex]\oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha}[/tex]

for any piecewise Jordan curve [tex]C[/tex].

2. Relevant equations

1. Green's Theorem

2. [tex]\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}[/tex] for [tex]\nabla f,\nabla g[/tex]

3. The attempt at a solution

I need some general direction on this one...

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# Homework Help: Closed curve line integral of gradient using Green's Theorem

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