Verify the conclusion of Green’s Theorem by evaluating both sides of Equations (3) and (4) for the field F = Mi + Nj. Take the domains of integration in each case to be the disk R: x² + y² ≤ a² and its bounding circle C: r = (a cos t)i + (a sin t)j, 0 ≤ t ≤ 2π.

F = -x²yi + xy²j

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ƏN fF-T ds = 6M dx + N dy = [[ (N-1) de c dx dy ax ay C R Counterclockwise circulation Curl integral (3)