<s>[INST] Polar Coordinates (Area enclosed) 
Find the common area enclosed by the curves
  $$r= 3 - 2 \cos \theta$$
  $$r= 2$$

My attempt, 
Area$$=4\pi-\int_{\frac{\pi}{3}}^{\frac{5\pi}{3}}\frac{1}{2}(4-(3-2\cos \theta)^2)d\theta$$
$$=36.753$$
Am I correct?
 [/INST] 
Area:
$$\begin{align}
2\left(\int_0^{\pi/3} \frac 12\big(\overbrace{3-2\cos\theta}^{\color{red}{r_1}}\big)^2 d\theta +\int_{\pi/3}^{\pi}\frac 12\cdot (\overbrace{\;\;2\;\;}^{\color{blue}{r_2}})^2 d\theta\right)
&=2\left(\frac {11}2\bigg(\frac {\pi}3-\frac{\sqrt{3}}2\bigg)+ \frac {4\pi}3\right)\\
&=11\bigg(\frac {\pi}3-\frac{\sqrt{3}}2\bigg)+\frac {8\pi}3\\
&=\color{red}{\frac {19}3\pi-\frac {11\sqrt{3}}2}\\
&=\color{red}{10.37}\end{align}$$
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