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math_proof

  • 2 years ago

triple integrals in spherical coordinates

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  1. math_proof
    • 2 years ago
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    \[\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}(x^2+y^2+z^2)^{5/2}\]

  2. math_proof
    • 2 years ago
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    i know it going to be p^5 but what will the ingtegrals be

  3. zepdrix
    • 2 years ago
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    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? :)

  4. math_proof
    • 2 years ago
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    it just states that it is the unit ball

  5. zepdrix
    • 2 years ago
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    oh i see :)

  6. math_proof
    • 2 years ago
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    so i guess the theta will be from 0 to 2pi right?

  7. zepdrix
    • 2 years ago
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    \[z= \rho \cos \phi\]\[x=\rho \cos \theta \sin \phi\]\[y=\rho \sin \theta \sin \phi\] \[(x^2+y^2+z^2)=(\rho^2)\] 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).

  8. zepdrix
    • 2 years ago
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    \[\huge \int\limits_{\theta=0}^{2\pi}\int\limits_{\phi=0}^{\pi}\int\limits_{\rho=0}^{1}\rho^5 (\rho^2 \sin \phi d \rho d \phi d \theta)\] Somethinggggg like that. Thinkinggg..

  9. math_proof
    • 2 years ago
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    yeap its right thanks

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