We need to find the volume of the solid bounded by the cylinder with the equation z^2 + y^2 = 4 and the plane x + y = 2, in the first octant (x,y,z all positive). Firstly, I am trying to visualize the graphs. From what I can tell, the cylinder is centered around the x-axis and has a radius of 2. It seems move along the x-axis infinitely. The plane intersects the cylinder at y=2, z=0. Visualizing this is tough and I haven't been able to find a graphing program that is sufficient. Now, we have performed double integrals of solids over general two dimensional regions. I just cannot even think of where to start with this problem. Any help setting me in the right direction would be extremely helpful!