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Câu hỏi: Biết ${\int\limits_{0}^{1}{f\left( x \right)\text{d}x=-2}}$ và ${\int\limits_{0}^{5}{f\left( x \right)\text{d}x=3},}$ khi đó ${\int\limits_{1}^{5}{2f\left( x \right)\text{d}x}}$ bằng
A. $10.$
B. $5.$
C. $2.$
D. $1.$
A. $10.$
B. $5.$
C. $2.$
D. $1.$
Ta có: $\int\limits_{0}^{5}{f\left( x \right)\text{d}x=}\int\limits_{0}^{1}{f\left( x \right)\text{d}x+\int\limits_{1}^{5}{f\left( x \right)\text{d}x}}$ $\Rightarrow \int\limits_{1}^{5}{f\left( x \right)\text{d}x=}\int\limits_{0}^{5}{f\left( x \right)\text{d}x-}\int\limits_{0}^{1}{f\left( x \right)\text{d}x=}3-\left( -2 \right)=5$
Vậy $\int\limits_{1}^{5}{2f\left( x \right)\text{d}x=}2\int\limits_{1}^{5}{f\left( x \right)\text{d}x=}2.5=10.$
Vậy $\int\limits_{1}^{5}{2f\left( x \right)\text{d}x=}2\int\limits_{1}^{5}{f\left( x \right)\text{d}x=}2.5=10.$
Đáp án A.
