Compute the Flux of the Vector Field $\overrightarrow { \vec { H } } = \vec { y } i + 2 z \vec { j }$

Short Answer

Compute the flux of the vector field $\overrightarrow { \vec { H } } = \vec { y } i + 2 z \vec { j }$ over the surface S, which is oriented upward and given, for 0 $\le$ s $\le$ 1, 0 $\le$ t $\le$ 2 by $x = s + t ^ { 2 } , y = s ^ { 2 } , z = 4 t$