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Triple Integral

  1. Jul 21, 2009 #1
    Problem: Evaluate (leave in rectangular coordinates):
    [tex]

    \int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz\,dy\,dx
    [/tex]
     
  2. jcsd
  3. Jul 21, 2009 #2
    Well, start slow. Can you evaluate this integral?
    [tex]
    \int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz
    [/tex]
     
  4. Jul 21, 2009 #3
    [tex]

    2\int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\2{\sqrt{1-x^2-y^2}}}\,dy\,dx
    [/tex]

    Supposedly it's easier to make a subtitution u = 1-x^2 at this point but I don't see how...
     
    Last edited: Jul 21, 2009
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