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) = xy i + 8x2 j + yz k S is the surface z = xey, 0 ≤ x ≤ 1, 0 ≤ y ≤ 3, with upward orientation