Question

Решите интеграл от cosx^2dx
2)230 — 220 × 0,5 =
3)8:2*(2+2)=

Answer 1

$1)\ \ \int cos^2x\, dx=\int \dfrac{1+cos2x}{2}\, dx=\dfrac{1}{2}\, x+\dfrac{1}{4}\, sin2x+C\\\\\\2)\ \ 230-220\cdot 0,5=230-110=120\\\\3)\ \ 8:2\cdot (2+2)=8:2\cdot 4=\dfrac{8}{2}\cdot 4=4\cdot 4=16\\\\4)\ \ \sqrt{200}\, cos(-\dfrac{4\pi }{3})\cdot sin(-\dfrac{\pi}{4})=10\sqrt{2}\cdot cos\dfrac{2\pi}{3}\cdot (-sin\dfrac{\pi}{4})=\\\\=-10\sqrt2\cdot cos(\pi +\dfrac{\pi}{3})\cdot \dfrac{\sqrt2}{2}=-10\sqrt2\cdot (-cos\dfrac{\pi}{3})\cdot \dfrac{\sqrt2}{2}=$

$=10\sqrt2\cdot \dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}=\dfrac{10\cdot 2}{2\cdot 2}=5$