Let C be a positively oriented, piecewise smooth, simple closed curve and let D be the region enclosed by the curve. If P and Q have continuous first order partial derivatives on D then, ∫c(Pdx+Qdy) =
1
∫∫D (dQ/dx-dP/dy) dA
2
∫(dQ/dx)dA
3
∫∫(dy/dp)dA
4
∫D (dQ/dx-dP/dy) dA