Найти площадь фигуры, ограниченной линиями: y=cos⁡x,y=0,x=-π/3,x=π/6. Created by ilakrasnogrudov. algebra-ru

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ilakrasnogrudov @ilakrasnogrudov

August 2022 1 3 Report

Найти площадь фигуры, ограниченной линиями:
y=cos⁡x,y=0,x=-π/3,x=π/6

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Artem112

Verified answer

$\int\limits^\frac{\pi}{6} _{-\frac{\pi}{3} } {\cos x} \, dx =\left \sin x\right|^\frac{\pi}{6} _{-\frac{\pi}{3} }=\sin\dfrac{\pi}{6} -\sin\left(-\dfrac{\pi}{3}\right)=$

$=\sin\dfrac{\pi}{6} +\sin\dfrac{\pi}{3}=\dfrac{1}{2} +\dfrac{\sqrt{3} }{2} =\dfrac{1+\sqrt{3} }{2}$

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