Find the flux of the vector field F = <-y, x, 1> across the cylinder y = x^2, for 0 <= x <= 1, 0 <= z <= 4. Normal vectors point in the general direction of the positive y-axis.
Parametrize the surface using u = x and v = z. Set up the integral that gives the flux as a double integral over a region R in the uv-plane.
∬ F ∙ n dS = ∬ du dv
(Type exact answers.)