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Possible Duplicate:
Will moving differentiation from inside, to outside an integral, change the result?

In analysis there is such

theorem: Let $f:[0,1]\times\mathbb{R}\to\mathbb{R}$ $(x,\lambda)\mapsto f(x,\lambda)$ such continuous function of independent variable $x$ and real parameter $\lambda$ that all partial derivatives exist and continuous everywhere. And let $I(\lambda)=\int_{0}^{1}f(x,\lambda)dx$ Then $\frac{d}{d\lambda}I(\lambda)=\int_{0}^{1}\frac{\partial f(x,\lambda)}{\partial\lambda}dx.$

Is there some analogous statement for multiple integrals?

Thanks

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    @QiaochuYuan and Aspirin: http://math.stackexchange.com/questions/12909/2012-04-01

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