Question

Evaluate the surface integral double 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) = xyi + 12x^2j + yzk
S is the surface z = xe^y, 0 less than or equal to x less than or equal to 1, 0 less than or equal to y less than or equal to 4, with upward orientation.