Question Number 192543 by peter frank last updated on 20/May/23
Answered by leodera last updated on 20/May/23
$$\Delta\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left({x}\right)}{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{dx} \\ $$$$\Delta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {dx} \\ $$$$\Delta\:=\:\frac{\pi}{\mathrm{4}} \\ $$$$ \\ $$$$ \\ $$