My professor gave me the following formula for integration by parts in my multivariable calculus class. He said that we wouldn't find it in our book, and he didn't provide a proof. I have tried to work through it, but I am still left with one question: Why is it necessary that the curve is closed (the line integral)?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int\int_{D}f(x,y)\frac{\partial g}{\partial x,y}dA=\oint_{\Sigma}f(x,y)g(x,y)\mathbf{n}\cdot d\mathbf{s}-\int\int_{D}g(x,y)\frac{\partial f}{\partial x,y}dA[/tex]

For lack of a better notation, I used [tex]\frac{\partial f}{\partial x,y}[/tex] to represent the fact that the derivative could be with respect to either x or y.

Thanks for your help.

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# Integration by Parts in Several Variables

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