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) = x i + y j + 7 k
S is the boundary of the region enclosed by the cylinder x^2 + z^2 = 1 and the planes y=0 and x+y = 2.

Answer 1

I wish I knew how to do that

Answer 2

start with drawing the region ... easy way, use Gauss divergence theorem. if you wish to find the flux through all surfaces, it's messy ... there are couple of techniques to do that. but start with drawing region.

Answer 3

it's messy ...