If the area of the region \ (x, y):-1 leq x leq 1,0 leq y leq a+e x -e -x , a 0 \ is frac e 2 +8 e+1 e , then the value of a is :

Mathematics · Area under the Curves

JEE Main 2025 — 23 January, Evening Shift — Question 8

If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq a+e^{|x|}-e^{-x}, a>0\right\}$

is $\frac{e^{2}+8 e+1}{e}$ , then the value of $a$ is :

required area is $a+\int_{0}^{1}\left(a+e^{x}-e^{-x}\right) d x$

$a+\left[ax+e^{x}+e^{-x}\right]_{0}^{1}$

$2\mathrm{a}+\mathrm{e}+\mathrm{e}^{-1}-1-1=\mathrm{e}+8+\frac{1}{\mathrm{e}}$

$2 \mathrm{a}=10 \Rightarrow \mathrm{a}=5$

Answer key and solution verified before publishing.

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