Right now I'm so confused! I tried projecting it, the way I know how and got the annoying answer of 8/3...I'm getting closer! Could someone point out where I've gone wrong in my working? Thanks:
Project onto xy plane.
F=(0,2x,z) but z=0 therefore F=(0,2x,0)
Sec gamma = (2,1,2)/[|(2,1,2).(0,0,1)|]
sec gamma = (1,1/2,1)
Now F.sec gamma = x
Then we know the limits are:
x: 0 -> (2-y/2)
y: 0 -> 4
So Integral (0->4) Integral (0->(2-y/2)) x dxdy
Which when I evaluate it gives me 8/3!