cos+|cos| 합성 적분

$\displaystyle \begin{aligned} \text{준식} ) & = \int _{\frac{\pi}{6}} ^{\pi} {} \left\{ \cos \left( 2 x - \frac{\pi}{6} \right) + \left| \cos \left( 2 x - \frac{\pi}{6} \right) \right| \right\} dx \end{aligned}$ $\displaystyle = \int _{\frac{\pi}{6}} ^{\frac{\pi}{3}} {} 2 \cos \left( 2 x - \frac{\pi}{6} \right) dx + \int _{\frac{5 \pi}{6}} ^{\pi} {} 2 \cos \left( 2 x - \frac{\pi}{6} \right) dx$ $\displaystyle = \left[ \sin \left( 2 x - \frac{\pi}{6} \right) \right] _{\frac{\pi}{6}} ^{\frac{\pi}{3}} + \left[ \sin \left( 2 x - \frac{\pi}{6} \right) \right] _{\frac{5 \pi}{6}} ^{\pi}$ $\displaystyle = \left( \sin \frac{\pi}{2} - \sin \frac{\pi}{6} \right) + \left( \sin \frac{11 \pi}{6} - \sin \frac{3 \pi}{2} \right) = 1$