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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integration by Parts in Several Variables

Loading...

Similar Threads - Integration Parts Several | Date |
---|---|

I Integration by parts | Dec 12, 2017 |

A Integration by parts of a differential | Jul 28, 2017 |

I Integrating sqrt(x) cos(sqrt(x)) dx | Dec 18, 2016 |

I Integration by Parts without using u, v | Nov 30, 2016 |

I Vector integration by parts | May 18, 2016 |

**Physics Forums - The Fusion of Science and Community**