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 + 9 k
S is the boundary of the region enclosed by the
cylinder x2 + z2 =
1 and the planes y = 0
and x + y = 5