Question: Evaluate the surface integral S F d S for the given vector field F and the oriented surface S . In other words, find the

Evaluate the surface integral

S

FdS

for the given vector fieldFand the oriented surfaceS. In other words, find the flux ofFacrossS. For closed surfaces, use the positive (outward) orientation.

F(x,y,z) =xyi+yzj+zxk

Sis the part of the paraboloidz=6x2y2that lies above the square0x1, 0y1,

and has upward orientation

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