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Advanced MathQ&A LibraryEvaluate the surface integral SSF 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 = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientationStart your trial now! First week only $4.99!*arrow_forward*

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Evaluate the surface integral SS_{F} 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 = 2 − x^{2} − y^{2} that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation

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