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Câu hỏi: Nếu $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}=-3$ thì $\int\limits_{1}^{4}{f\left( \dfrac{x}{2} \right)\text{d}x}$ bằng
A. $5$.
B. $-6$.
C. $-1$.
D. $-\dfrac{3}{2}$.
A. $5$.
B. $-6$.
C. $-1$.
D. $-\dfrac{3}{2}$.
Đặt $t=\dfrac{x}{2}\Rightarrow \text{d}x=\dfrac{1}{2}\text{d}x\Rightarrow \text{d}x=2\text{d}x$.
Đổi cận $x=1\Rightarrow t=1; x=4\Rightarrow t=2$.
Suy ra $\int\limits_{1}^{4}{f\left( \dfrac{x}{2} \right)\text{d}x}=2\int\limits_{1}^{2}{f\left( t \right)\text{d}x=2\left( -3 \right)=-6}$.
Đổi cận $x=1\Rightarrow t=1; x=4\Rightarrow t=2$.
Suy ra $\int\limits_{1}^{4}{f\left( \dfrac{x}{2} \right)\text{d}x}=2\int\limits_{1}^{2}{f\left( t \right)\text{d}x=2\left( -3 \right)=-6}$.
Đáp án B.