Mathematics - Definite Integration Question with Solution | TestHub

$f(x)=\frac{1}{e^{x-1}}=e^{1-x}$
\begin{array}{c|c}\mathrm{f}(\mathrm{x})=2 & \mathrm{f}(\mathrm{x})=1 \\\frac{1}{\mathrm{e}^{\mathrm{x}-1}}=2 & \mathrm{x}=1 \\\mathrm{x}=1-\ln 2 &\end{array}
$f(0)=e^1=2.71$
$f\left(e^3\right)=e^{1-e^3}\in (0,1)$
$\mathrm{I}={\int }_0^{1-\ell \mathrm{n}2}2\mathrm{dx}+{\int }_{1-\ell \mathrm{n}2}^{1}1\mathrm{dx}+{\int }_1^{{\mathrm{e}}^3}0\mathrm{dx}$
$=2(1-\ell n2-0)+1(1-1+\ln 2)+0$
$\alpha -\ln 2=2-\ln 2$
$\alpha =2$
${\alpha }^3=8$