may i know what mistake have i made?

given that the vector field F(x,y,z) = < -y,x,x-2y>. use stokes theorem to compute the upward flux of curl F across z=1-x^2 -y^2 with z>0.

what i did:

curl F =<-2,-1,2>

using stoke theorem, integral F. dr = double integral curl F dS = triple integral grad (Curl F) dxdydz =0 as grad (curl F)=0

may i know why this doesnt work?

thanks!