Find the volume V of the solid that: lies under the paraboloid $$z=4−x^2−y^2$$ and above the xy-plane. Also, what will change during your process if the solid lies inside and outside the cylinder given by $x^2+y^2≤1$ and $x^2+y^2≥1$, respectively? Set-up the integrals only in these two cases and sketch the corresponding regions.
So, I solved the initial question by integrating twice using polar coordinates, but the second half of this question has me confused. I'm not sure why anything changes if you give a function and state that the solid exists on both sides of it. Wouldn't the function not serve as a bound for the solid?