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

* Hướng dẫn giải

\(\int\limits_5^2 {\left[ {2 - 4f\left( x \right)} \right]{\rm{d}}x} = 2\int\limits_5^2 {{\rm{d}}x} - 4\int\limits_5^2 {f\left( x \right){\rm{d}}x} = \left. {2x} \right|_5^2 + 4\int\limits_2^5 {f\left( x \right){\rm{d}}x} = 2.\left( {2 - 5} \right) + 4.10 = 34\)