anonymous
  • anonymous
triple integrals in spherical coordinates
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}(x^2+y^2+z^2)^{5/2}\]
anonymous
  • anonymous
i know it going to be p^5 but what will the ingtegrals be
zepdrix
  • zepdrix
Do we have a region we're integrating over? D: Any boundaries like z=0, x=0 or anything? :O Or you're more concerned with just converting it correctly right now? :)

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anonymous
  • anonymous
it just states that it is the unit ball
zepdrix
  • zepdrix
oh i see :)
anonymous
  • anonymous
so i guess the theta will be from 0 to 2pi right?
zepdrix
  • zepdrix
\[z= \rho \cos \phi\]\[x=\rho \cos \theta \sin \phi\]\[y=\rho \sin \theta \sin \phi\] \[(x^2+y^2+z^2)=(\rho^2)\] Oh oh you said you already figured that part out :) my bad. Yah theta will range from 0 to 2pi. Phi from 0 to pi I think... and Rho from 0 to our radius (1 since it's the UNIT ball).
zepdrix
  • zepdrix
\[\huge \int\limits_{\theta=0}^{2\pi}\int\limits_{\phi=0}^{\pi}\int\limits_{\rho=0}^{1}\rho^5 (\rho^2 \sin \phi d \rho d \phi d \theta)\] Somethinggggg like that. Thinkinggg..
anonymous
  • anonymous
yeap its right thanks

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