Mathematics - Definite Integration Question with Solution | TestHub

$\mathrm{I}={\int }_0^{\pi /2}\frac{2^{\sin \mathrm{x}}}{2^{\sin x}+2^{\cos \mathrm{x}}\mathrm{dx}}$ $\mathrm{I}={\int }_0^{\pi /2}\frac{2^{\sin (\pi /2-\mathrm{x})}}{2^{\sin (\pi /2-\mathrm{x})}+2^{\cos (\pi /2-\mathrm{x})}\mathrm{dx}}$ $=\int \frac{2^{\cos \mathrm{x}}}{2^{\cos \mathrm{x}}+2^{\sin \mathrm{x}}}\mathrm{dx}\Rightarrow 21={\int }_0^{\pi /2}\mathrm{d}\mathrm{x}=\frac{\pi }{2}\Rightarrow 1=\frac{\pi }{4}$