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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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Advance 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) = x i + y j + z4 k


S is the part of the cone z =

x2 + y2

beneath the plane

z = 1

with downward orientation

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