Verified Solution • 2025–26 Session moderate

QJEEM25Ma0245: JEE Main 2025 Mathematics - Class 12 JEEM25Ma0245 Solution: The area of the region enclosed by the curves and -axis is :

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

Multiple Choice Options

A $1+\log _{\mathrm{e}} 2$
B $\log _{\mathrm{e}} 2$
C $1-\log _{\mathrm{e}} 2$
D $2 \log _{\mathrm{e}} 2-1$

Step-by-Step Verified Solution

JEE Main 2025 (Online) 24th January Evening Shift Mathematics - Area Under The Curves Question 2 English Explanation

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

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