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Math Help - triple integral

  1. #1
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    triple integral

    triple integral( xy dxdydz)
    through the quadrant of the unit sphere shell
    x^2+y^2+z^2= 1

    i m not sure about the upper limit of theta, phi, when changing variables.

    i think, theta goes from 0 to pi
    phi goes from 0 to half pi?
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    triple integral( xy dxdydz)
    through the quadrant of the unit sphere shell
    x^2+y^2+z^2= 1

    i m not sure about the upper limit of theta, phi, when changing variables.

    i think, theta goes from 0 to pi
    phi goes from 0 to half pi?
    If you mean the first octant( where x,y,z are positive)

    \int_{0}^{\pi/2}\int_{0}^{\pi/2}\int_{0}^{1}\left( \rho\sin(\phi)\cos(\theta)\right) \left( \rho\sin(\phi)\sin(\theta)\right)\rho^2\sin(\phi)d  \rho d\phi d\theta
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