Question

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

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 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,

and has upward orientation

Math   Calculus   
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