Cho hàm số \(f\left( x \right) = \left\{ \begin{array}{l}x + 1 & {\rm{khi}} & x \ge 0\\{e^{2x}} & {\rm{khi}} & x \le 0\end{arra

* Hướng dẫn giải

\(I = \int\limits_{ - 1}^0 {f\left( x \right){\rm{d}}x}  + \int\limits_0^2 {f\left( x \right){\rm{d}}x}  = \int\limits_{ - 1}^0 {{e^{2x}}{\rm{d}}x}  + \int\limits_0^2 {\left( {x + 1} \right){\rm{d}}x}  = \frac{{9{e^2} - 1}}{{2{e^2}}}.\)