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

$\int\limits_{0}^{2}{\left[ 2f\left( x \right)+x \right]dx=5}\Leftrightarrow 2\int\limits_{0}^{2}{f\left( x \right)dx+\int\limits_{0}^{2}{x}dx=5}\Leftrightarrow 2\int\limits_{0}^{2}{f\left( x \right)dx+\dfrac{{{x}^{2}}}{2}\left| \begin{aligned}
& 2 \\
& 0 \\
\end{aligned} \right.=5}\Rightarrow \int\limits_{0}^{2}{f\left( x \right)dx=\dfrac{3}{2}}$