Nếu \(\int\limits_{1}^{3}{\left[ 2f\left( x \right)+1 \right]}dx=5\) thì \(\int\limits_{1}^{3}{f\left( x \right)dx}\) bằng

* Hướng dẫn giải

\(\int\limits_{1}^{3}{\left[ 2f\left( x \right)+1 \right]dx=}2\int\limits_{1}^{3}{f\left( x \right)dx+}\int\limits_{1}^{3}{dx}\)

\(\Leftrightarrow 5=2\int\limits_{1}^{3}{f\left( x \right)dx+}x\left| \begin{align} & 3 \\ & 1 \\ \end{align} \right.\)

\(\Leftrightarrow 5=2\int\limits_{1}^{3}{f\left( x \right)dx+}2\)

\(\Leftrightarrow \int\limits_{1}^{3}{f\left( x \right)dx=\frac{3}{2}}\)