QJEEM25Ma4dc0: JEE Main 2025 Mathematics - Class 12 JEEM25Ma4dc0 Solution: If the area of the region is , then the value of is :

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QJEEM25Ma4dc0: JEE Main 2025 Mathematics - Class 12 JEEM25Ma4dc0 Solution: If the area of the region is , then the value of is :

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 :

Multiple Choice Options

A 7
B 5
C 6
D 8

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Accepted Answer

JEE Main 2025 (Online) 23rd January Evening Shift Mathematics - Area Under The Curves Question 4 English Explanation

$\begin{aligned} required area is a + \int_{0}^{1} (a + e^{x} - e^{- x}) d x \\ a + {[a + e^{x} + e^{- x}]}_{0}^{1} \\ 2 a + e - 1 + e^{- 1} - 1 = e + 8 + \frac{1}{e} \\ 2 a = 10 \Rightarrow a = 5 \end{aligned}$

QJEEM25Ma4dc0: JEE Main 2025 Mathematics - Class 12 JEEM25Ma4dc0 Solution: If the area of the region is , then the value of is :

Multiple Choice Options

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