Here's the problem :

Let

and

.

1)Show by a justification that

.

2)Deduce that

.

My attempt : almost none. My first problem is : they never defined the function

. If I assume it's a volume function then they seem to ask me to calculate the volume of a 4 dimensional solid (or whatever it is called), which seems senseless. I realize that

is the projection of

in the 3 dimensional space.

Also, I recognize the integrand to be the positive

that satisfy the first inequation. So

really seems a volume since there's the multiplication by 2 in front of the triple integral so that my instinct tells me that this covers the

. I may not be clear here, but that's how I understand the problem.

If you understand it better than I, feel free to reformulate it so that I can understand it.