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Câu hỏi: Cho hàm số $f\left( x \right)$ liên tục trên $\mathbb{R}$ và $\int\limits_{0}^{6}{f\left( x \right)\text{d}x=12}$. Tính $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}$.
A. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=6$.
B. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=4$.
C. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=-4$.
D. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=36$.
A. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=6$.
B. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=4$.
C. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=-4$.
D. $\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=36$.
Đặt $t=3x\Rightarrow dt=3dx$.
$\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=\int\limits_{0}^{6}{f(t)\dfrac{dt}{3}}=\dfrac{1}{3}\int\limits_{0}^{6}{f(x)dx}=4$.
$\int\limits_{0}^{2}{f\left( 3x \right)\text{d}x}=\int\limits_{0}^{6}{f(t)\dfrac{dt}{3}}=\dfrac{1}{3}\int\limits_{0}^{6}{f(x)dx}=4$.
Đáp án B.