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Câu hỏi: Nếu $\int\limits_{0}^{3}{2f\left( x \right)\text{d}x}=6$ thì $\int\limits_{0}^{3}{\left[ 2-\dfrac{f\left( x \right)}{3} \right]\text{d}x}$ bằng
A. 7.
B. 5.
C. 0.
D. 4.
A. 7.
B. 5.
C. 0.
D. 4.
Ta có: $\int\limits_{0}^{3}{2f\left( x \right)\text{d}x}=6$ $\Rightarrow \int\limits_{0}^{3}{f\left( x \right)\text{d}x}=3$.
Vậy: $\int\limits_{0}^{3}{\left[ 2-\dfrac{f\left( x \right)}{3} \right]\text{d}x}=\int\limits_{0}^{3}{\text{2d}x}-\dfrac{1}{3}\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=6-1=5$.
Vậy: $\int\limits_{0}^{3}{\left[ 2-\dfrac{f\left( x \right)}{3} \right]\text{d}x}=\int\limits_{0}^{3}{\text{2d}x}-\dfrac{1}{3}\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=6-1=5$.
Đáp án B.