Question

решите срочно ,4 задание !!!

Answer 1

Ответ:

$\int\limits^{\pi /3}_0\, \dfrac{5}{sin^2(x+\frac{\pi}{3})}\, dx=-5\cdot ctg\Big(x+\dfrac{\pi}{3}\Big)\Big|_0^{\pi /3}=-5\cdot \Big(ctg\dfrac{2\pi}{3}-ctg\dfrac{\pi}{3}\Big)=\\\\\\=-5\cdot \Big(-\dfrac{\sqrt3}{3}-\dfrac{\sqrt3}{3}\Big)=5\cdot \dfrac{2\sqrt3}{3}=\dfrac{10\sqrt3}{3}$