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Câu hỏi: Nếu $\int\limits_{0}^{1}{2f\left( x \right)\text{d}x=6}$ thì $\int\limits_{0}^{1}{\left[ \dfrac{1}{3}f\left( x \right)+2x \right]\text{d}x}$ bằng
A. $4$.
B. $7$.
C. $3$.
D. $2$.
A. $4$.
B. $7$.
C. $3$.
D. $2$.
Ta có $\int\limits_{0}^{1}{\left[ \dfrac{1}{3}f\left( x \right)+2x \right]\text{d}x}=\dfrac{1}{3}\int\limits_{0}^{1}{f\left( x \right)\text{d}x}+2\int\limits_{0}^{1}{x\text{d}x}=\dfrac{1}{6}\int\limits_{0}^{1}{2f\left( x \right)\text{d}x}+\left. {{x}^{2}} \right|_{0}^{1}=\dfrac{1}{6}.6+1=2$.
Đáp án D.