Mathematics - Area Under Curves Question with Solution | TestHub

$|\mathrm{x}|=1$ $\therefore \mathrm{x}=\pm 1$ $\therefore \mathrm{y}={\mathrm{xe}}^{|\mathrm{x}|}=\left\{\begin{array}{l}\mathrm{x}\cdot {\mathrm{e}}^{-\mathrm{x}},-1<\mathrm{x}<0\\ \mathrm{x}\cdot {\mathrm{e}}^{\mathrm{x}},0<\mathrm{x}<1\end{array}\right\}$ $\therefore$ Required area $=\left|{\int }_{-1}^0{\mathrm{xe}}^{-\mathrm{x}}\mathrm{dx}+{\int }_0^1{\mathrm{xe}}^{\mathrm{x}}\mathrm{dx}\right|$ $=\left|{\left[-\mathrm{x}\cdot {\mathrm{e}}^{-\mathrm{x}}-{\mathrm{e}}^{-\mathrm{x}}\right]}_{-1}^0+{\left\{\mathrm{x}\cdot {\mathrm{e}}^{\mathrm{x}}-{\mathrm{e}}^{\mathrm{x}}\right\}}_0^1\right|$ $=|\{(0-1)-(1\cdot \mathrm{e}-\mathrm{e})\}|+|\{(\mathrm{e}-\mathrm{e})-(0-1)\}|$ $=1+1=2\mathrm{sq}$ units