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A very very long time ago I learned a technique for integrating vectors and those that are under the operations of the cross product/dot product. Now I remember that it was really straight forward for the dot product (I don't think the order matters in the integral), btu I forgot how to integrate a cross product integral. For instance

$\int \vec{u} \times \vec{v} dx = \vec{u} \times \int \vec{v} dx $

$\int \vec{u} \times \vec{v} dx = (\int \vec{u} dx) \times \vec{v} $

Does anyone know what identity I am thinking off?

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closed as off-topic by anorton, kigen, dfeuer, Dominic Michaelis, Johannes Kloos Nov 8 '13 at 6:47

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Perhaps you're thinking of what is sometimes called Stokes' theorem? [This is a special case, really.] –  Dylan Moreland Dec 23 '11 at 21:27
No, not Stoke's theorem. It's not any theorem. It was just an easy way to integrate vectors. It has nothing to do with curl or anything –  jak Dec 23 '11 at 21:37
This is just the linearity of the integral, in a special case. –  Mariano Suárez-Alvarez Dec 23 '11 at 21:44
It seems hard to make sense of $\vec u$ living outside of the integral then. Maybe someone more competent than I will have an interpretation! –  Dylan Moreland Dec 23 '11 at 21:52
I'm voting to close because it appears that the consensus in the comments is that the identities given are false (assuming $u$ and $v$ are functions of $x$). Thus, not much of an answer can be given... –  anorton Nov 8 '13 at 5:13

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