I have no idea what you mean by '"y^3" going to 0' or '"4" turning into 8pi' The anti-derivative of y^3 is, of course, y^4/4 but how does it "go to 0"? The anti-derivative of 4 (with respect to y) is 4y. How does that "turn into 8pi"? I also have a problem with "Over the region ". That is an unbounded region. You will certainly NOT give a finite result. Did you mean to say "less than or equal to 2"?