# Math Help - triple integral

1. ## 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?

2. 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)

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