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## sjmoneys96 one year ago find the total mass of the solid ball x^2+y^2+z^2=1. The ball has a mass density of 1/(1+x^2+y^2+z^2). I know that a conversion to spherical coordinates is needed but am unsure of how to do it.

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1. azr95

Let $\rho^2 = x^2+y^2+z^2$ and triple-integrate the density function over the domain$\rho \in [0,1]; \theta \in [0,2\pi]; \phi \in [0,\pi]$ So you should end up with something like$\int\limits_{0}^{2\pi}\int\limits_{0}^{\pi}\int\limits_{0}^{1}\frac{ 1 }{ 1+\rho^2 }d \rho d \phi d \theta$

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