Cho \(\int\limits_{1}^{2}{\left[ 3f\left( x \right)-2x \right]dx}=6\). Khi đó \(\int\limits_{1}^{2}{f\left( x \right)}dx\) bằng

* Hướng dẫn giải

\(\begin{array}{l} \int\limits_1^2 {\left[ {3f\left( x \right) - 2x} \right]dx} = 6 \Leftrightarrow 3\int\limits_1^2 {f\left( x \right)dx - 2\int\limits_1^2 {xdx} } = 6 \Leftrightarrow 3\int\limits_1^2 {f\left( x \right)dx - 2.} \left. {\frac{{{x^2}}}{2}} \right|_1^2 = 6\\ \Leftrightarrow 3\int\limits_1^2 {f\left( x \right)dx = 9 \Leftrightarrow } \int\limits_1^2 {f\left( x \right)dx = 3} . \end{array}\)