r=(x,y,2-2x-y)
rx=(1,0,-2)
ry=(0,1,-1)
|rx*ry|=|(2,1,1)|=6^.5
6^.5SS(x^2+y-(2-2x-y))dxdy [0,1]x[0,2]
6^.5SS(x^2+2x+2y-2)dxdy
6^.5S(1/3+1+2y-2)dy
6^.5S(-2/3+2y)dy
-2/3(2)+4=8/3
(8/3)(6)^.5