Find the Flux Of Across the Surface of the Solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1$

Short Answer

Find the flux of $\mathbf { F } ( x , y , z ) = \left( x ^ { 2 } z + \frac { 1 } { \ln ( y + 3 ) } \right) \mathbf { i } + \left( x y z + \frac { 1 } { ( y + 3 ) } \right) \mathbf { j } + \left( x z ^ { 2 } + \frac { z } { ( y + 3 ) ^ { 2 } } \right) \mathbf { k }$ across the surface of the solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1$ .