Chapter 17.6, Problem 46E

Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface.

46.    F = 〈e^–y, 2z, xy〉 across the curved sides of the surface $S=\left\{\left(x,y,z\right):z=\cos y,\left|y\right|\le \pi ,0\le x\le 4\right\}$; normal vectors point upward.