Let $\displaystyle \overline{{{F}}}=<{x}^{{2}}{e}^{{{y}{z}}},{x}{e}^{{{x}{z}}},{z}^{{2}}{e}^{{{x}{y}}}>$.

Use Stokes' Theorem to evaluate $\displaystyle \int\int_{{S}}{c}{u}{r}{l}\overline{{{F}}}\cdot{d}\overline{{{S}}}$, where

$\displaystyle {S}$ is the hemisphere $\displaystyle {x}^{{2}}+{y}^{{2}}+{z}^{{2}}={4},\ {z}\ge{0}$, oriented upwards