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Câu hỏi: Cho hàm số $f\left( x \right)$ liên tục trên $\mathbb{R}$ thỏa mãn $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=2$ và $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}=3$. Tính tích phân $\int\limits_{0}^{3}{f\left( \left| 2-x \right| \right)\text{d}x}$ bằng?
A. $7$.
B. $5$.
C. $3$.
D. $-3$.
A. $7$.
B. $5$.
C. $3$.
D. $-3$.
$\int\limits_{0}^{3}{f\left( \left| 2-x \right| \right)\text{d}x}=\int\limits_{0}^{2}{f\left( \left| 2-x \right| \right)\text{d}x}+\int\limits_{2}^{3}{f\left( \left| 2-x \right| \right)\text{d}x}=\int\limits_{0}^{2}{f\left( 2-x \right)\text{d}x}+\int\limits_{2}^{3}{f\left( x-2 \right)\text{d}x}$
$=\int\limits_{0}^{2}{f\left( x \right)\text{d}x}+\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+2\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=3+2.2=7$.
$=\int\limits_{0}^{2}{f\left( x \right)\text{d}x}+\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\int\limits_{1}^{2}{f\left( x \right)\text{d}x}+2\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=3+2.2=7$.
Đáp án A.