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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Originally Posted by szpengchao 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) $\displaystyle \int_{0}^{\pi/2}\int_{0}^{\pi/2}\int_{0}^{1}\left( \rho\sin(\phi)\cos(\theta)\right) \left( \rho\sin(\phi)\sin(\theta)\right)\rho^2\sin(\phi)d \rho d\phi d\theta$
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