Q: "Evaluate the triple integral $f (x,y,z) = z(x^2+y^2+z^2)^\frac{-3}2$ over part of the ball $x^2+y^2+z^2 \leqslant 36$ defined by $z \geqslant 3$"
I have yet to encounter an equation written in this form and was wondering if my bounds were
$x=[ 0 , 6 ] , y =[ 0 , 6 ] , z=[ 3 , 6 ]$. If not could you explain how i should approach a question where i am given a $\leqslant$ instead of a $=$
Hints: First, the $\le$ makes no difference. In any case you are integrating over some portion of the ball, and the presence or absence of the boundary is not relevant here.
Second, draw a picture. Once you've done that, consider the portion of the solid that lies above $z=3$. What region in the $xy$-plane does that portion lie over? That region will determine the bounds of integration for $x$ and $y$.
Third, are you expected to perform this integration in some set of coordinates other than Cartesian?