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