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Câu hỏi: Nếu $\int\limits_{-1}^{2}{f\left( x \right)\text{d}x}=2$ và $\int\limits_{-1}^{2}{g\left( x \right)\text{d}x}=-1$ thì $\int\limits_{-1}^{2}{\left[ x+2f\left( x \right)+3g\left( x \right) \right]\text{d}x}$ bằng
A. $\dfrac{17}{2}$.
B. $\dfrac{7}{2}$.
C. $\dfrac{5}{2}$.
D. $\dfrac{11}{2}$.
A. $\dfrac{17}{2}$.
B. $\dfrac{7}{2}$.
C. $\dfrac{5}{2}$.
D. $\dfrac{11}{2}$.
Ta có $\int\limits_{-1}^{2}{\left[ x+2f\left( x \right)+3g\left( x \right) \right]\text{d}x}=\int\limits_{-1}^{2}{\text{xd}x}+2\int\limits_{-1}^{2}{f\left( x \right)\text{d}x}+3\int\limits_{-1}^{2}{g\left( x \right)\text{d}x}=\dfrac{3}{2}+2.2+3\left( -1 \right)=\dfrac{5}{2}$.
Đáp án C.