Question asks to evaluate the surface integral for the given $\displaystyle F$ and $\displaystyle S$ with stokes theorem.

$\displaystyle F= [z^2, x^2, y^2], s: z^2 = x^2 + y^2$ for $\displaystyle y >= 0$, $\displaystyle 0<=z<=2$

My question is that in transformation from x,y to u,v shouldn't there be jacobian multiplied ? I dont see it anywhere in the solution.