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If I want to change the following integral from Cartesians to Polars:

$\int_{-\infty}^\infty\int_{-\infty}^\infty (x-a)^2+(y-b)^2\,\,dx\,dy$

in a way such that we are centered at $(a,b)$, so $(x-a)^2+(y-b)^2=r^2$,

Is the polar form simply $\int_0^{2\pi}\int_0^\infty r^3 \,\,dr\,d\theta$?

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    Can this kind of "Is ... correct/true?" question be improved further?2011-12-27

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The answer to your question:

Yes.