Let F = (2², x + z, y³ ) and let S'be the upper half of the ellipsoid +y + z² = 1 oriented by outward- pointing normals. Use Stokes' Theorem to compute ffs curl(F) · dS as the circulation around the boundary, and then use Green's Theorem to compute the integral over the projection of the ellipsoid in the xy-plane (note: you'll get the same answer; the point is to demonstrate that there are two ways of simplifying this problem by using both theorems).

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