Question Number 127726 by mnjuly1970 last updated on 01/Jan/21
$$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{evaluate}:: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{ln}\left({cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)−{ln}\left({cos}\left(\frac{{y}}{\mathrm{2}}\right)\right)}{{cos}\left({x}\right)−{cos}\left({y}\right)}\right){dxdy} \\ $$$$ \\ $$