The area of the region enclosed by the curves $y = \mathrm{e}^{x}$, $y = \left| \mathrm{e}^{x} - 1 \right|$ and $y$-axis is: (1) $1 - \log_{e} 2$ (2) $\log_{e} 2$ (3) $1 + \log_{e} 2$ (4) $2 \log_{e} 2 - 1$
The area of the region enclosed by the curves $y = \mathrm{e}^{x}$, $y = \left| \mathrm{e}^{x} - 1 \right|$ and $y$-axis is:\\
(1) $1 - \log_{e} 2$\\
(2) $\log_{e} 2$\\
(3) $1 + \log_{e} 2$\\
(4) $2 \log_{e} 2 - 1$