Use the Divergence Theorem to Find the Flux of the Vector

Essay

Use the Divergence Theorem to find the flux of the vector field $\vec { F } = \left( 4 x ^ { 3 } + 4 y z \right) \vec { i } + \left( 4 y ^ { 3 } + 8 x z \right) \vec { j } + \left( 4 z ^ { 3 } + 16 y x \right) \vec { k }$ through the cube 0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1, 0 $\le$ z $\le$ 1.