JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region \(\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq a+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}\gt0\right\}\) is \(\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}\), then the value of \(a\) is :
- A 8
- B 7
- C 5
- D 6
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y \in\left[0, a+e^{|x|}-e^{-x}\right] \\ & \text { (i) If } x \geq 0 \Rightarrow y \in\left(0, a+e^x-\frac{1}{e^x}\right) \\ & \text { if } x…
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