Cho $\int\limits_{2}^{5}{f\left( x \right)\text{d}x}=10$. Kết quả $\int\limits_{5}^{2}{\left[ 2-4f\left( x \right) \right]\text{d}x}$ bằng

Ta có: $\int\limits_{5}^{2}{\left[ 2-4f\left( x \right) \right]\text{d}x}=-\int\limits_{2}^{5}{\left[ 2-4f\left( x \right) \right]\text{d}x}=-2\int\limits_{2}^{5}{\text{d}x}+4\int\limits_{2}^{5}{f\left( x \right)}\text{d}x$.
$ =-\left. 2x \right|_{2}^{5}+4\int\limits_{2}^{5}{f\left( x \right)\text{d}x=}-6+40=34$.