вычислить интеграл: ∫от π/8 до π/4 cos4xdx

Решите задачу:

$\\\int \limits_{\frac{\pi}{8}}^{\frac{\pi}{4}} {\cos 4x}\, dx=(*)\\ t=4x\\ dt=4\, dx\\ \int \limits_{\frac{\pi}{8}}^{\frac{\pi}{4}} \frac{1}{4}{\cos t}\, dt=\\ \frac{1}{4}\int \limits_{\frac{\pi}{8}}^{\frac{\pi}{4}} {\cos t}\, dt=\\ \frac{1}{4}\Big[\sin t\Big]_{\frac{\pi}{8}}^{\frac{\pi}{4}}=\\ (*)=\frac{1}{4}\Big[\sin 4x\Big]_{\frac{\pi}{8}}^{\frac{\pi}{4}}=\\ \frac{1}{4}(\sin (4\cdot\frac{\pi}{4})-\sin (4\cdot\frac{\pi}{8}))=\\ \frac{1}{4}(\sin \pi-\sin \frac{\pi}{2})=\\ \frac{1}{4}(0-1)=\\ \frac{1}{4}\cdot(-1)=\\ -\frac{1}{4}$