Nếu \(\int\limits_{0}^{2}{\left[ 2f\left( x \right)+x \right]dx=5}\) thì \(\int\limits_{0}^{2}{f\left( x \right)dx}\) bằng

* Hướng dẫn giải

\(\int\limits_0^2 {\left[ {2f\left( x \right) + x} \right]dx = 5} \Leftrightarrow 2\int\limits_0^2 {f\left( x \right)dx + \int\limits_0^2 x dx = 5} \Leftrightarrow 2\int\limits_0^2 {f\left( x \right)dx + \frac{{{x^2}}}{2}\left| \begin{array}{l} 2\\ 0 \end{array} \right. = 5} \Rightarrow \int\limits_0^2 {f\left( x \right)dx = \frac{3}{2}} \)