Nếu \(\int\limits_{1}^{3}{f\left( x \right)\text{d}x}=-3\) và \(\int\limits_{2}^{3}{f\left( x \right)\text{d}x}=4\) thì \(\int\limits_{1}^{2}{f\left( x \right)\text{d}x}\) bằng

* Hướng dẫn giải

Ta có : \(\int\limits_{1}^{3}{f\left( x \right)\text{d}x\,=\,\int\limits_{1}^{2}{f\left( x \right)\text{d}x}}\,+\,\int\limits_{2}^{3}{f\left( x \right)\text{d}x} \Leftrightarrow \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=\,\int\limits_{1}^{3}{f\left( x \right)\text{d}x}-\,\int\limits_{2}^{3}{f\left( x \right)\text{d}x}\)

\(\Leftrightarrow  \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=-3-4=-7\).