Chapter 10 - Section 10.2 - Areas and Lengths in Polar Coordinates - 10.4 Exercises - Page 673: 27

$\pi$

$A=\frac{1}{2}\int_{0}^{\pi/3}(3cos\theta)^{2}d \theta-\frac{1}{2}\int_{0}^{\pi/3}(1+cos\theta)^{2}d \theta$ $=\frac{1}{2}[3\theta+2sin2\theta-2sin\theta]_{0}^{\pi/3}$ $=\frac{\pi}{2}$ Therefore, the area of the whole crescent is $2*\frac{\pi}{2} =\pi$