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Câu hỏi: Cho $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=2$, $\int\limits_{0}^{2}{f\left( x \right)\text{d}x}=5$. Tích phân $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}$ bằng
A. $1$.
B. $2$.
C. $-1$.
D. $3$.
A. $1$.
B. $2$.
C. $-1$.
D. $3$.
Ta có: $\int\limits_{0}^{2}{f\left( x \right)\text{d}x}=\int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{1}^{2}{f\left( x \right)\text{d}x}$
$\Rightarrow \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=\int\limits_{0}^{2}{f\left( x \right)\text{d}x}-\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=5-2=3$
$\Rightarrow \int\limits_{1}^{2}{f\left( x \right)\text{d}x}=\int\limits_{0}^{2}{f\left( x \right)\text{d}x}-\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=5-2=3$
Đáp án D.