Compute the Flux of the Vector Field $\vec { F } = y \vec { i } + ( x + y ) \vec { j } + z \vec { k }$

Essay

Compute the flux of the vector field $\vec { F } = y \vec { i } + ( x + y ) \vec { j } + z \vec { k }$ through the surface S that is the part of the surface $z = x ^ { 2 } - y ^ { 2 }$ above the disk $x ^ { 2 } + y ^ { 2 } \leq 1$ , oriented in the positive z-direction.