My normal vector calculated is <1,2,3> since my surface parametrization is <1-2y-3z,y,z> Ty = <-2,1,0> Tz=<-3,0,1> --> TyxTz=<1,2,3> I integrate the dot product of <1,2,3><2y,-3z,4-8y-12z> = -22y-42z+12 from z=0 to z=-2/3y+1/3 and y=0 to 1/2. The answer i get is 11/36. What went wrong?
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you didn't take the curl of F.