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

F = x²y³i + j + zk

C: The intersection of the cylinder x² + y² = 4 and the hemisphere x² + y² + z² = 16, z ≥ 0, counterclockwise when 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: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)