Evaluate the surface integral, 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) = xzey i − xzey j + z kS is the part of the plane x + y + z = 3 in the first octant and has upward orientation

Question

Evaluate the surface integral, 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(xyz) = xzey i − xzey j + z k
S is the part of the plane x + y + z = 3 in the first octant and has upward orientation

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