Cho hàm số y=f(x) liên tục, có đạo hàm trên [-1;0] .

* Hướng dẫn giải

$\begin{array}{l}f\text{'}\left(x\right)=(3x^2+2x).e^{-f\left(x\right)}\iff \frac{f\text{'}\left(x\right)}{e^{-f\left(x\right)}}=3x^2+2x\iff f\text{'}\left(x\right).e^{f\left(x\right)}=3x^2+2x\\ \Rightarrow \underset{-1}{\overset{0}{\int }}f\text{'}\left(x\right).e^{f\left(x\right)}dx=\underset{-1}{\overset{0}{\int }}\left(3x^2+2x\right)dx\\ \iff {\left.e^{f\left(x\right)}\right|}_{-1}^0={\left.\left(x^3+x^2\right)\right|}_{-1}^0=0\iff e^{f\left(0\right)}-e^{f\left(-1\right)}=0\iff e^{f\left(0\right)}=e^{f\left(-1\right)}\end{array}$