## tdabboud Group Title find the average value f(x,y,z) = xyz over the spherical region x^2 _ y^2 + z^2 <=1 3 years ago 3 years ago

1. dipankarstudy Group Title

take $x=rcos \phi \cos \theta, y=r \cos \phi \sin \theta, z=rcos \theta$

2. tdabboud Group Title

and you plug those into the integral but what are the bounds

3. dipankarstudy Group Title

then $f _{avg}=3/(4\pi)\int\limits_{r=0}^{1}\int\limits_{\theta=0}^{\pi}\int\limits_{\phi=0}^{2\pi}r ^{3}\sin ^{2}\theta \cos \theta \sin \phi \cos \phi drd \theta d \phi$ probably this will give you 0

4. dipankarstudy Group Title