Triple Integral

  • Thread starter Ions
  • Start date
  • #1
2
0
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]
 

Answers and Replies

  • #2
537
3
Well, start slow. Can you evaluate this integral?
[tex]
\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz
[/tex]
 
  • #3
2
0
[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:

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