Find the flux of the following vector field across the given surface with the specified orientation. Use either an explicit or a parametric description of the surface.
F = ⟨-y,x,1⟩ across the cylinder y = 3x^2, for 0 ≤ x ≤ 2, 0 ≤ z ≤ 4; normal vectors point in the general direction of the positive y-axis.
The flux is
(Simplify your answer.)