What is the area bounded by \(y=e^{|x|}\) and the lines \(|x|=1\) and \(y=0\)?
\((2e-2)\) square units
By symmetry of \(y=e^{|x|}\) about the y-axis, the required area is \(2\displaystyle\int_{0}^{1}e^{x}\,dx=2\big[e^{x}\big]_{0}^{1}=2(e-1)=2e-2\) square units.
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\({\rm{f}}\left( {\rm{x}} \right) = {\rm{x}}\left| {\rm{x}} \right| - 1{\rm{\;and\;g}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{3{\rm{x}}}}{2},{\rm{\;x}} > 0}\\ {2{\rm{x}},{\rm{\;x}} \le 0} \end{array}} \right.\)
Where do the curves intersect?
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