Cho \(\int\limits_{1}^{2}{f\left( x \right)\text{d}x=-3}, \int\limits_{2}^{5}{f\left( x \right)\text{d}x=5}\) và \(\int\limits_{1}^{5}{g\left( x \right)\text{d}x=6}\). Tính tích ph...

* Hướng dẫn giải

Ta có \(\int\limits_{1}^{5}{f\left( x \right)\text{d}x=}\int\limits_{1}^{2}{f\left( x \right)\text{ }}dx+\int\limits_{2}^{5}{f\left( x \right)dx}=-3+5=2\)

\(I=\int\limits_{1}^{5}{\left[ 2.f\left( x \right)-g\left( x \right) \right]\text{d}x}=2\int\limits_{1}^{5}{f\left( x \right)\text{d}x}-\int\limits_{1}^{5}{g\left( x \right)\text{d}x}=-2\)