Question: Use the Divergence Theorem to evaluate \[\iint\limits_{S}{\ F\ \cdot \ N\ d\,s}\] and find the outward flux of F through the surface of the solid bounded by the graphs of the equations:

\[\begin{aligned} & F\,\left( \,x,\ y,\ z\, \right)\quad =\quad {{x}^{\,2}}\ z\ i\quad -\quad y\ j\quad +\quad x\ y\ z\ k \\ & \\ & S:\quad x\ =\ 0,\quad x\ =\ a,\quad y\ =\ 0,\quad y\ =\ a,\quad z\ =\ 0,\quad z\ =\ a \\ \end{aligned}\]