Question

Imi puteti spune va rog unde gresesc...?

Answer 1

arcsin(sinx) = x, x ∈ [0, π/2]

arcsin(sinx) = pi-x, x ∈ [π/2, π]

$\displaystyle \int_0^{\pi} \arcsin(\sin x)\, dx =\\ =\int_0^{\frac{\pi}{2}} x\, dx + \int_{\frac{\pi}{2}}^{\pi} (\pi-x)\, dx =...=\dfrac{\pi^2}{4}$