(Solved): Use the Divergence Theorem to calculate the surface integral \( \iint_{S} \mathrm{~F} \cdot d \mat ...

Use the Divergence Theorem to calculate the surface integral \( \iint_{S} \mathrm{~F} \cdot d \mathbf{S} \). \[ F(x, y, z)=e^{x} \sin (y) i+e^{x} \cos (y) j+y z^{2} \mathbf{k} \] \( S \) is the surface of the box bounded by the planes \( x=0, x=3, y=0, y=2, z=0 \), and \( z=1 \).