7) ∫ cos x dx;

7) Вычислим интеграл:

$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{2}} cos(x) dx = sin(x) \Big|_{-\frac{\pi}{4}}^{\frac{\pi}{2}} = sin(\frac{\pi}{2}) - sin(-\frac{\pi}{4}) = 1 - (-\frac{\sqrt{2}}{2}) = 1 + \frac{\sqrt{2}}{2}$$.

Ответ: $$1 + \frac{\sqrt{2}}{2}$$