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