The area of the region enclosed by the curves y=e^x,y=|e^x-1| and y-axis is :

Question

The area of the region enclosed by the curves $y={e}^{x},y=|{e}^{x}-1|$ and $y$-axis is :

Accepted Answer

$$\begin{aligned}
&\text { For Area } \int_{-\ln 2}^0\left[e^x-\left(1-e^x\right)\right] d x\
&\begin{aligned}
& \int_{-\operatorname{nn} 2}^0\left(2 \mathrm{e}^{\mathrm{x}}-1\right) \mathrm{dx}=\left[2 \mathrm{e}^{\mathrm{x}}-\mathrm{x}\right]_{-\ln 2}^0 \
& =(2-(1+\ell \mathrm{n} 2)) \
& =1-\ell \mathrm{n} 2
\end{aligned}
\end{aligned}$$

Solutions · 1