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 + yz j + zx k
S is the part of the paraboloid
z = 6 − x^2 − y^2 that
lies above the square 0 ≤ x ≤ 1,
0 ≤ y ≤ 1,
and has upward orientation.