Biết \(\int\limits_{0}^{2}{f\left( x \right)dx}=3,\,\int\limits_{0}^{5}{f\left( x \right)dx}=4\), khi đó \(\int\limits_{2}^{5}{2f\left( x \right)dx}\) bằng

* Hướng dẫn giải

\(\int\limits_2^5 {2f\left( x \right)dx}  = 2\int\limits_2^5 {f\left( x \right)dx}  = \,2\left[ {\int\limits_0^5 {f\left( x \right)dx}  - \int\limits_0^2 {f\left( x \right)dx} } \right] = 2\left( {4 - 3} \right) = 2\)