Use Stokes' theorem to evaluate
$$ \iint_S \operatorname{curl} F \cdot \hat{n}\, dS $$
where $F =\langle xyz, x, e^{xy} \cos(z)\rangle$
$S$ is the hemisphere $x^2+y^2+z^2=25$ for $z ≥ 0$ oriented upward.
I know how to compute the curl of the vector field. I don't know how to get the normal. I'm a bit confused about what it is.
Once I have the dot product of the $\operatorname{curl} F$ and the normal then I can redefine the sphere in terms of $\theta$ and $\phi$ (spherical coordinates) and I can compute the integral, no?
I specifically want to complete this problem using stokes' theorem.