Question

Buna . Are cineva habar de rezolvarea a acestui Exercițiu? Este un Exercițiu de algebra din facultate

Answer 1

$\int\limits^1_{-1} { \dfrac{1}{ \sqrt{1^2-x^2} } } \, dx = arcsin \Big(\dfrac{x}{1}\Big)\Big|_{-1}^1 = arcsin (x)\Big|_{-1}^1 = \\ =arcsin(1) - arcsin(-1) = \dfrac{\pi}{2} -\Big(- \dfrac{\pi}{2}\Big)=\dfrac{\pi}{2}+\dfrac{\pi}{2}= \pi$