Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the

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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) = xzey i − xzey j + z k S is the part of
the plane x + y + z = 9 in the first octant and has downward
orientation.