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Let ~ be the curve given by the intersection of the plane = = 2 and the cone = = vx2 + yz counter- clockwise
Let ~ be the curve given by the intersection of the plane = = 2 and the cone = = vx2 + yz counter- clockwise oriented as viewed from above. Let the vector field F = (r' -y, 42, '). Use Stokes' theorem to find the circulation of F around ~ by integrating over (i) the surface of the cone (ii) the flat disk of radius 2 centered on the z-axis and lying in the plane z = 2
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