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

Mathematics · Area under the Curves

JEE Main 2025 — 24 January, Evening Shift — Question 15

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

For Area $\int_{-\ell n 2}^{0}\left[e^{x}-\left(1-e^{x}\right)\right] d x$

$\int_{-\ell \mathrm{n} 2}^{0}\left(2 e^{x}-1\right) d x=\left[2 e^{x}-x\right]_{-\ell \mathrm{n} 2}^{0}$

$=(2-(1+\ell \mathrm{n} 2))$

$=1-\ell \mathrm{n} 2$

Answer key and solution verified before publishing.

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