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Q: Verify Stokes' theorem for F = (-y, x, 0) with C the unit circle in the xy-plane and S the disk. Line integral: r(t) = (cos t, sin t, 0). F dot r' = (-sin t, cos t, 0) dot (-sin t, cos t, 0) = sin^2 t + cos^2 t = 1. Integral 0 to 2pi of 1 dt = 2pi. Surface: curl F = (0,0,2). n = (0,0,1). curl F dot n = 2. Integral over disk: 2 times area = 2pi. Match!