Cho \(\int\limits_{ - 1}^2 {f\left( x \right)dx} = 2,\) \(\int\limits_{ - 1}^2 {g\left( x \right)dx} = - 1\). Khi đó \(I = \int\limits_{ - 1}^2 {\left[ {x + 2f\left( x \right) - 3g\left( x \right)} \right]} dx\) bằng

Hướng dẫn giải

Ta có \(I = \int\limits_{ - 1}^2 {\left[ {x + 2f\left( x \right) - 3g\left( x \right)} \right]} dx = \frac{{{x^2}}}{2}\left| {_{\scriptstyle\atop\scriptstyle - 1}^{\scriptstyle2\atop\scriptstyle}} \right. + 2\int\limits_{ - 1}^2 {f\left( x \right)dx} - 3\int\limits_{ - 1}^2 {g\left( x \right)dx} \)

\( = \frac{3}{2} + 2.2 - 3\left( { - 1} \right) = \frac{2}.\)

Chọn B.