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Câu hỏi: Cho $\int\limits_{1}^{2}{f\left( {{x}^{2}}+1 \right)x.dx}=2$. Khi đó $\int\limits_{2}^{5}{f\left( x \right)dx}$ bằng
A. 2.
B. 1.
C. $-1$.
D. 4.
A. 2.
B. 1.
C. $-1$.
D. 4.
Ta có $2=\dfrac{1}{2}\int\limits_{1}^{2}{f\left( {{x}^{2}}+1 \right)d\left( {{x}^{2}}+1 \right)}=\dfrac{1}{2}\int\limits_{2}^{5}{f\left( t \right)dt}=\dfrac{1}{2}\int\limits_{2}^{5}{f\left( x \right)dx}\Rightarrow \int\limits_{2}^{5}{f\left( x \right)dx}=4$.
Đáp án D.