Answer
See the explanation below.
Work Step by Step
The area enclosed by a curve can be written as: $\int \int_D dA $
Here, $D$ defines the set of vector points enclosed by curve $C$.
An area enclosed by a curve can be calculated as:
$\int \int_D dA =\oint_Cx dy=-\oint_C y dx=\frac{1}{2}\oint_Cx dy-ydx$
