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Câu hỏi: Nếu $\int\limits_{2}^{5}{f\left( x \right)\text{d}x}=4$ và $\int\limits_{5}^{2}{g\left( x \right)\text{d}x}=5$ thì $\int\limits_{2}^{5}{\left[ 2f\left( x \right)+g\left( x \right) \right]\text{d}x}$ bằng
A. $13$
B. $3$
C. $x-1$
D. $-3$
A. $13$
B. $3$
C. $x-1$
D. $-3$
Ta có $\int\limits_{5}^{2}{g\left( x \right)\text{d}x}=5\Rightarrow \int\limits_{2}^{5}{g\left( x \right)\text{d}x}=-5$.
Khi đó $\int\limits_{2}^{5}{\left[ 2f\left( x \right)+g\left( x \right) \right]\text{d}x}=2\int\limits_{2}^{5}{g\left( x \right)\text{d}x}+\int\limits_{2}^{5}{g\left( x \right)\text{d}x}=2.4-5=3$.
Khi đó $\int\limits_{2}^{5}{\left[ 2f\left( x \right)+g\left( x \right) \right]\text{d}x}=2\int\limits_{2}^{5}{g\left( x \right)\text{d}x}+\int\limits_{2}^{5}{g\left( x \right)\text{d}x}=2.4-5=3$.
Đáp án B.