(Solved): both parts please Find the average value of the function \( f(x, y, z)=x y z \) on the unit sphere i ...

Find the average value of the function \( f(x, y, z)=x y z \) on the unit sphere in the first octant. Set up the surface integral of f over the first octant of the unit sphere. Use increasing limits of integration. The average value is \( \frac{1}{4 \pi} \). (Type an exact answer.)