Mathematics - Area under the curve Question with Solution | TestHub

$\begin{array}{rl}& y\in \left[0,a+e^{|x|}-e^{-x}\right]\\ & \text{ (i) If }x\ge 0\Rightarrow y\in \left(0,a+e^x-\frac{1}{e^x}\right)\\ & \text{ if }x<0\Rightarrow y\in \left(0,a+e^{-x}-e^{-x}\right)\\ & \Rightarrow y\in (0,a)\end{array}$

$\begin{array}{rl}& \text{ Area }=(a)+{\int }_0^1\left(a+e^x-e^{-x}\right)dx=\frac{e^2+8e+1}{e}\\ & =a+{\left(ax+e^x+e^{-x}\right)|}_0^1=e+8+\frac{1}{e}\\ & =a+\left(a+e+\frac{1}{e}-2\right)=e+\frac{1}{e}+8\\ & \Rightarrow 2a-2=8\Rightarrow a=5\end{array}$