Nếu \(\int\limits_{ - 1}^2 {f\left( x \right)d{\rm{x}}} = 2\) và \(\int\limits_{ - 1}^2 {g\left( x \right)d{\rm{x}}} = - 1\) thì \(\int\limits_{ - 1}^2 {\left[ {x + 2f\left( x \...

* Hướng dẫn giải

\(\int\limits_{ - 1}^2 {\left[ {x + 2f\left( x \right) - 3g\left( x \right)} \right]d{\rm{x}}} = \int\limits_{ - 1}^2 {x{\rm{dx}}} + 2\int\limits_{ - 1}^2 {f\left( x \right)d{\rm{x}}} - \int\limits_{ - 1}^2 {g\left( x \right)d{\rm{x}}} = \left. {\frac{{{x^2}}}{2}} \right|_{ - 1}^2 + 4 + 3 = \frac{3}{2} + 7 = \frac{{17}}{2}\)