Cho \(\int\limits_{a}^{c}{f\left( x \right)\text{d}x=50}\), \(\int\limits_{b}^{c}{f\left( x \right)\text{d}x=20}\). Tính \(\int\limits_{b}^{a}{f\left( x \right)\text{d}x}\).

* Hướng dẫn giải

Ta có \(\int\limits_{b}^{a}{f\left( x \right)\text{d}x} =\int\limits_{b}^{c}{f\left( x \right)\text{d}x}+\int\limits_{c}^{a}{f\left( x \right)\text{d}x}=\int\limits_{b}^{c}{f\left( x \right)\text{d}x}-\int\limits_{a}^{c}{f\left( x \right)\text{d}x} =20-50=-30\).