Use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C in the indicated direction.

C: The circle in which the plane z = -y meets the sphere x² + y² + z² = 4, counterclockwise as viewed from above

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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: $ - fx F.dr = Counterclockwise circulation V X F.ndo Curl integral (4)