Cho - 2}^1 {f(x)\,dx = - 2}^1 {g(x)\,dx = - 2} } \). Tính - 2}^1 {\left( {1 - f(x) + 3g(x)} \right)} \,dx\).

* Hướng dẫn giải

Ta có: \(\int\limits_{ - 2}^1 {\left( {1 - f(x) + 3g(x)} \right)} \,dx \)

\(= \left( x \right)\left| {_{ - 2}^1} \right. - \int\limits_{ - 2}^1 {f\left( x \right)} \,dx + 3\int\limits_{ - 2}^1 {g\left( x \right)} \,dx \)

\(= 3 - 1 + 3.\left( { - 2} \right) =  - 4\)