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theBTMANIAC
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Homework Statement
Prove that ∫u∇v dl = - ∫v∇u dl
Both integrals are over closed surfaces.
Homework Equations
The question is being asked in a chapter over Stoke's Theorem. However, I'm confused because I think found the solution without invoking the theorem... Which leads to...
The Attempt at a Solution
I used integration by parts to derive
∫u∇v dl = uv - ∫v∇u dl
However since it's over a closed surface, I believe (uv) goes to zero. Is this the correct proof? Thanks.