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

Short Answer

Find the flux of the vector field $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + \mathbf { k }$ across the paraboloid given by $x = u \cos v , y = u \sin v , z = 1 - u ^ { 2 }$ with $1 \leq u \leq 2,0 \leq v \leq 2 \pi$ and upward orientation: