Compute the Flux of the Vector Field ${ \vec { F } } = ( x - 3 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 4 x \vec { k }$

Short Answer

Compute the flux of the vector field ${ \vec { F } } = ( x - 3 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 4 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented downward.