Cho biết \(\int\limits_{0}^{3}{f\left( x \right)}\text{d}x=3,\,\,\int\limits_{0}^{5}{f\left( t \right)}\text{d}t=10\). Tính \(\int\limits_{3}^{5}{2f\left( z \right)}\text{d}z\).

* Hướng dẫn giải

\(\int\limits_3^5 {2f\left( z \right)} {\rm{d}}z = 2\int\limits_3^5 {f\left( z \right)} {\rm{d}}z = 2\left[ {\int\limits_0^5 {f\left( z \right)} {\rm{d}}z - \int\limits_0^3 {f\left( z \right)} {\rm{d}}z} \right] = 2\left( {10 - 3} \right) = 14\)