Mathematics - Area Under Curves Question with Solution | TestHub

By symmetry about $y=x$, the area between the two curves inside the square equals the square minus twice the area above $y=e^x$ within the square. Since $e^x\le 2$ for $x\le \ln 2$ : area above $={\int }_0^{\ln 2}(2-$ $e^x)dx={\left[2x-e^x\right]}_0^{\ln 2}=2\ln 2-1$. So the enclosed area is $4-2(2\ln 2-1)$ and the remaining area is $4-[4-2(2\ln 2-1)]=2(2\ln 2-1)$.