1. The problem statement, all variables and given/known data Prove that ∫u∇v dl = - ∫v∇u dl Both integrals are over closed surfaces. 2. Relevant 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... 3. 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.