264. $\int_{0}^{\pi / 3} \sin x d x$. 265. $\int_{\pi / 6}^{\pi / 2} \cos x d x . \quad 266 . \int_{0}^{\pi / 4} \cos 2 x d x$.
Solution. $\int_{0}^{\pi / 4} \cos 2 x d x=\left.\frac{1}{2} \sin 2 x\right|_{0} ^{\pi / 4}=\frac{1}{2}\left(\sin 2 \cdot \frac{\pi}{4}-\sin 2 \cdot 0\right)=$ $=\frac{1}{2} \sin \frac{\pi}{2}=\frac{1}{2} \cdot 1=\frac{1}{2}$.