Question

find the average value f(x,y,z) = xyz over the spherical region x^2 _ y^2 + z^2 <=1

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

please check it....

Answer 5

okay I am working it right now

Answer 6

i cant understand