8) ∫ sin x dx.

8) Вычислим интеграл:

$$\int_{\frac{\pi}{6}}^{\pi} sin(x) dx = -cos(x) \Big|_{\frac{\pi}{6}}^{\pi} = -cos(\pi) - (-cos(\frac{\pi}{6})) = -(-1) + cos(\frac{\pi}{6}) = 1 + \frac{\sqrt{3}}{2}$$.

Ответ: $$1 + \frac{\sqrt{3}}{2}$$