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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S....

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Basic Math

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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