ImageShack® - Online Photo and Video Hosting
I dont know how to get the 3 limits, could someone teach me how to do it? Thanks
ImageShack® - Online Photo and Video Hosting
I dont know how to get the 3 limits, could someone teach me how to do it? Thanks
In spherical coordinates we have
$\displaystyle x=r\sin(\theta)\cos(\phi) \quad y=r\sin(\theta)\sin(\phi) \quad z=r\cos(\theta)$
and
$\displaystyle x^2+y^2+z^2=r^2$
Since you want a hemisphere the azimuthal angle theta will be in
$\displaystyle \theta \in \left[0,\frac{\pi}{2} \right]$
$\displaystyle \phi \in [0,2\pi]$
$\displaystyle r \in [0,a]$
Don't forget the Jacobian is
$\displaystyle dV=r^2\sin(\theta)\dr d\theta d\phi$