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Câu hỏi: Cho $\int\limits_{1}^{2}{\left[ 3f\left( x \right)+2x \right]\text{d}x}=12$. Khi đó $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}$ bằng
A. $3$.
B. $2$.
C. $\dfrac{11}{3}$.
D. $\dfrac{10}{3}$.
Ta có
$\int\limits_{1}^{2}{\left[ 3f\left( x \right)+2x \right]\text{d}x}=12\Leftrightarrow 3\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+\int\limits_{1}^{2}{2x\text{d}x}=12\Leftrightarrow 3\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+3=12\Leftrightarrow \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=3$.
A. $3$.
B. $2$.
C. $\dfrac{11}{3}$.
D. $\dfrac{10}{3}$.
Ta có
$\int\limits_{1}^{2}{\left[ 3f\left( x \right)+2x \right]\text{d}x}=12\Leftrightarrow 3\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+\int\limits_{1}^{2}{2x\text{d}x}=12\Leftrightarrow 3\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+3=12\Leftrightarrow \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=3$.
Đáp án A.