f(x,y,z) = y; W is the region bounded by the plane x+y+z=2;cylinder x^2+z^2=1. and y=0.

What I have set up isL
4 int(0 to 1) int(0 to sqrt(1-x^2)) int(0 to 1-x-y) y dydzdx.

But solving this is pretty cumbersome.
Any other ideas?