1. The problem statement, all variables and given/known data - Sketch the region V of 3-space that is bounded above and below by the two surfaces z=Z1(x,y) = 0 and z=Z2(x,y)=1+x^2+y^2 and where the domain of these functions is the region R in the xy plane enclosed by the four lines y=x, y=-x, y=2+x and y=2-x -Calculate the volume using a double integral namely http://img145.imageshack.us/img145/2705/q3tv3.png [Broken] 3. The attempt at a solution For the first part I have firstly drawn the four lines in the xy plane http://img239.imageshack.us/img239/7389/q3ct1.png [Broken] Obviously I make it 3d by adding the top (i.e. 1+x^2+y^2 for -1 ≤ x ≤1 and 0 ≤ y ≤ 2) My question is regarding the volume integral. It is difficult to nominate the y bounds due to the nature of the 4 lines. I am thinking I should split the area into two sections, bisected by the y axis such that the volume can be calculated by: http://img73.imageshack.us/img73/8666/q3ao8.png [Broken] Am I on the right track?