is a maximum.

Solution: Let E be any region on which for all (x,y,z) in E. Then this integral is non-negative on E. Furthermore, if F is any region that contains E and for all (x,y,z) in F then the volume over F is greater than the volume over E.

So, the largest value of the integral occurs when E is the largest region such that

for all (x,y,z) in E. This is the set of (x,y,z) such that

.

No Maple Code on this problem.