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    • 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
      • 11 months ago
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      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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