Đáp án đúng: C
Giải chi tiết:Đặt hai tích phân \(C = \int\limits_1^2 {f\left( x \right){\rm{d}}x} ,\,\,\,D = \int\limits_1^2 {g\left( x \right){\rm{d}}x} \)
Khi đó \(A = 1 \Leftrightarrow 3\,\int\limits_1^2 {f\left( x \right){\rm{d}}x} + 2\int\limits_1^2 {g\left( x \right){\rm{d}}x} = 1 \Leftrightarrow 3C + 2D = 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right).\)
Và \(B = - \,3 \Leftrightarrow 2\,\int\limits_1^2 {f\left( x \right){\rm{d}}x} - \int\limits_1^2 {g\left( x \right){\rm{d}}x} = - \,3 \Leftrightarrow 2C - D = - \,3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right).\)
Từ \(\left( 1 \right),\,\,\left( 2 \right)\) suy ra \(\left\{ \matrix{ 3C + 2D = 1 \hfill \cr 2C - D = - \,3 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ C = - {5 \over 7} \hfill \cr D = {{11} \over 7} \hfill \cr} \right. \Rightarrow \int\limits_0^1 {f\left( x \right){\rm{d}}x} = - {5 \over 7}.\)
Chọn C.