Any help will be appreciated for the following question:
Question: Represent $\displaystyle \int_S \nabla \times \overrightarrow{F} \cdot d\overrightarrow{s}$, where $S$ is the hemisphere $x^2+y^2+z^2=4, z\geq 0$ as a definite integral for $\overrightarrow{F} = \left< e^x, sin(xy), ze^y \right>$.