Answer
$\oint_C x dy=-\oint C y dx=-\dfrac{1}{2} \oint (x dy-y \ dx)$
Work Step by Step
Let us consider that $R$ is plain region which is enclosed by a curve $C$ .
In order to find the area of $R$, we will use Green's Theorem such as:
$\oint_C x dy=-\oint C y dx$
or, $\oint_C x dy=-\oint C y dx=-\dfrac{1}{2} \oint (x dy-y \ dx)$
