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Multivariable CalculusEasySurface Integrals, Stokes & Divergence

Surface Integrals, Stokes & Divergence · Easy problem

Let F=(−3y,3x,z2)\mathbf F = (-3y, 3x, z^2) and let CC be the circle x2+y2=1x^2 + y^2 = 1 in the plane z=2z = 2, oriented counterclockwise when viewed from above. Use Stokes' theorem to find ∮CF⋅dr\oint_C \mathbf F\cdot d\mathbf r. Give an exact answer in terms of π\pi.