## Thomas' Calculus 13th Edition

$\frac{3\pi}{2}-4$
We calculate the area as follows: A=$4\int^{\pi/2}_0 \int^{1-cos\theta}_0 rdrd\theta$ =$2\int^{\pi/2}_0 (\frac{3}{2}-2cos\theta +\frac{cos2\theta}{2})d\theta$ =$\frac{3\pi}{2}-4$