그린 정리 사용:

\dfrac{\partial Q}{\partial x} - \dfrac{\partial P}{\partial y}= \dfrac{\partial}{\partial x}(-x) - \dfrac{\partial}{\partial y}(y)= -1 - 1 = -2.

\displaystyle \oint_{C} \mathbf{F}\cdot d\mathbf{r}= \iint_{D} (-2)\, dA= -2 \cdot (\text{Area of D})

= -2 \cdot \bigl(\pi (1)^2 \bigr)= -2\pi