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Câu hỏi: Nếu $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}=5$ và $\int\limits_{1}^{2}{\left[ 2f\left( x \right)+g\left( x \right) \right]\text{d}x}=13$ thì $\int\limits_{1}^{2}{g\left( x \right)\text{d}x}$ bằng
A. $-3$.
B. $-1$.
C. $1$.
D. $3$.
A. $-3$.
B. $-1$.
C. $1$.
D. $3$.
Ta có: $\int\limits_{1}^{2}{\left[ 2f\left( x \right)+g\left( x \right) \right]\text{d}x}=2\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+\int\limits_{1}^{2}{g\left( x \right)\text{d}x}=10+\int\limits_{1}^{2}{g\left( x \right)\text{d}x}=13\Rightarrow \int\limits_{1}^{2}{g\left( x \right)\text{d}x}=3$
Đáp án D.