Question

Срочно нужно помогите алгебру буду благодарна

Answer 1

$1)\; \; \int _{\frac{\pi}{3}}^{\pi }sin(\frac{x}{2}-\frac{\pi}{6})dx=-2cos(\frac{x}{2}-\frac{\pi}{6})|_{\frac{\pi}{3}}^{\pi }=\\\\=-2(cos\frac{\pi}{3}-cos\, 0)=-2(\frac{1}{2}-1)=1\\\\2)\; \; \int _{\frac{\pi}{3}}^{\pi}\frac{6\; dx}{cos^22x}=6\cdot \frac{1}{2}tg2x|_{\frac{\pi}{3}}^{\pi }=3(tg2\pi -tg\frac{2\pi}{3})=3(tg2\pi +tg\frac{\pi}{3})=\\\\=3(0+\sqrt3)=3\sqrt3$