Question

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + x j + z2 k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos(v) i + u sin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 2π