# Triple integral

• May 9th 2011, 08:52 AM
qwerty1234
Triple integral
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I dont know how to get the 3 limits, could someone teach me how to do it? Thanks :)
• May 9th 2011, 09:10 AM
TheEmptySet
Quote:

Originally Posted by qwerty1234
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I dont know how to get the 3 limits, could someone teach me how to do it? Thanks :)

In spherical coordinates we have

$x=r\sin(\theta)\cos(\phi) \quad y=r\sin(\theta)\sin(\phi) \quad z=r\cos(\theta)$

and

$x^2+y^2+z^2=r^2$

Since you want a hemisphere the azimuthal angle theta will be in

$\theta \in \left[0,\frac{\pi}{2} \right]$

$\phi \in [0,2\pi]$

$r \in [0,a]$

Don't forget the Jacobian is

$dV=r^2\sin(\theta)\dr d\theta d\phi$
• May 12th 2011, 04:32 AM
qwerty1234
thanks!