$$\begin{aligned} = & 24 \int_0^{\frac{\pi}{48}}-\sin \left(4 \mathrm{x}-\frac{\pi}{12}\right)+\int_{\pi / 48}^{\pi / 4} \sin \left(4 \mathrm{x}-\frac{\pi}{12}\right) \\ & +\int_0^{\frac{\pi}{6}}[0] \mathrm{dx}+\int_{\pi / 6}^{\pi / 4}[2 \sin \mathrm{x}] \mathrm{dx} \end{aligned}$$

$$\begin{aligned} & =24\left[\frac{\left(1-\cos \frac{\pi}{12}\right)}{4}-\frac{\left(-\cos \frac{\pi}{12}-1\right)}{4}\right]+\frac{\pi}{4}-\frac{\pi}{6} \\ & =24\left(\frac{1}{2}+\frac{\pi}{12}\right)=2 \pi+12 \\ & \alpha=12 \end{aligned}$$