1. The problem statement, all variables and given/known data My first problem is with 2ia) and 2ib), I got the correct answer, although not happy with my understanding of it. http://img826.imageshack.us/img826/1038/443pr.jpg [Broken] 3. The attempt at a solution (2ia and 2ib) The region that's of concern is the upper part between y = x^2 and y = 4 isn't it? I thought that since y ≤ 4 and y ≥ x^2, if it were the lower part then the bounds would reverse. Using that reasoning I used the new bounds for x as: [√y ≤ x ≤ 2] because I thought, x is not going to get any larger than 2, and it's lower limit at any given point in time is √y, when integrating that, it's obvious the answer is not going to be elementary, so I just edited the bounds: [0 ≤ x ≤ √y] which works out, the only problem with this is now the region would appear to be the lower half and not the upper half that I originally thought it was given the initial bounds. What's happening here? (2ii) For this one, I'm having trouble describing the region. It's a sphere with radius ≤ 1, and based on the cuts given, it appears to be some kind spherical wedge, or even a slice of pizza pie, if the bounds for z is not too big. Is that correct?