Use the Divergence Theorem to Find the Flux of the Vector

Essay

Use the Divergence Theorem to find the flux of the vector field ${ \vec { F } } = \left( y ^ { 2 } x - 3 z ^ { 2 } y \right) \vec { i } + \left( z ^ { 2 } y + z x ^ { 3 } \right) \vec { j } + \left( x ^ { 2 } z + y x \right) \vec { k }$ through the sphere x² + y² + z² = $1$ .