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 + 16x² j + yz k

S is the surface z = xe^y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 4, with upward orientation