Answer
$$\dfrac{3\pi}{2}-4$$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Area =\iint_D dA $
$=4\int^{\pi/2}_0 \int^{1-cos\theta}_0 \space r \space dr \space d\theta $
or, $=2\int^{\pi/2}_0 (\dfrac{3}{2}-2 \cos\theta +\dfrac{ \cos2\theta}{2})\space d\theta $
and $ Area=\dfrac{3\pi}{2}-4$
