Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x² - y², z ≥ 0, oriented with unit normal n pointing upward.

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THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)