[tex] \int\limits^1_{-1} {\max\{e^x;e^{-x}\}} \, dx =? \\ f:[-1;1]\rightarrow\mathbb{R}\\f(x)=\max\{e^x;e^{-x}\}\\f(x)= \left \{ {{e^{-x}\ \ ;\ \ x\in[-1;0)} \atop {e^x\ \ \ ;\ \ \ x\in[0;1]}} \right. \\ \\ \\ \int\limits^1_{-1} {f(x)} \, dx = \\ \\ \int\limits^0_{-1} {e^{-x}} \, dx + \int\limits^1_0 {e^x} \, dx = \\ \\ \\ -e^{-x}|_{-1}^0\ +\ e^x|_{0}^1\ = \\ -1+e+e-1=2(e-1) [/tex]
