JEE MAIN - Mathematics (2025 - 23rd January Evening Shift - No. 8)
If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq \mathrm{a}+\mathrm{e}^{|x|} \mid-\mathrm{e}^{-x}, \mathrm{a}>0\right\}$ is $\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}$, then the value of $a$ is :
7
5
6
8
Explanation
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$$\begin{aligned} & \text { required area is } a+\int_\limits0^1\left(a+e^x-e^{-x}\right) d x \\ & a+\left[a+e^x+e^{-x}\right]_0^1 \\ & 2 a+e-1+e^{-1}-1=e+8+\frac{1}{e} \\ & 2 a=10 \Rightarrow a=5 \end{aligned}$$
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