Cho hàm số f(x)=x+1 khi x lớn hơn bằng 0

* Hướng dẫn giải

Đáp án D

$$\begin{gathered} I=\underset{-1}{\overset{2}{\int }}f\left(x\right)d\text{x}=\underset{-1}{\overset{0}{\int }}f\left(x\right)d\text{x}+\underset{0}{\overset{2}{\int }}f\left(x\right)d\text{x}=\underset{-1}{\overset{0}{\int }}{e}^{2\text{x}}d\text{x}+\underset{0}{\overset{2}{\int }}(x+1)d\text{x}={\left.\frac{1}{2}{e}^{2\text{x}}\right|}_{-1}^0+{\left.\frac{{(x+1)}^2}{2}\right|}_0^2 \\ =\frac{9{\text{e}}^2-1}{2{\text{e}}^2} \end{gathered}$$.