Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S....
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Evaluate the surface integral
S
F · dS
for the given vector field F and the orientedsurface S. In other words, find the flux ofF across S. For closed surfaces, use thepositive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k
S is the part of the paraboloid
z = 6 − x2 − y2 that lies above the square0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has upward orientation
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