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Câu hỏi: Cho hàm số $f\left( x \right)$ có đạo hàm trên $\left[ -1;2 \right]$, biết $\int\limits_{1}^{2}{f\left( x \right)\text{d}x}=-1$, $\int\limits_{-1}^{2}{f\left( x \right)\text{d}x}=10$. Khi đó $\int\limits_{-1}^{1}{f\left( x \right)\text{d}x}$ là
A. $9.$
B. $11.$
C. $-10.$
D. $-11.$
A. $9.$
B. $11.$
C. $-10.$
D. $-11.$
Ta có: $\int\limits_{-1}^{2}{f\left( x \right)\text{d}x}=\int\limits_{-1}^{1}{f\left( x \right)\text{d}x}+\int\limits_{1}^{2}{f\left( x \right)\text{d}x}\Rightarrow \int\limits_{-1}^{1}{f\left( x \right)\text{d}x}=\int\limits_{-1}^{2}{f\left( x \right)\text{d}x}-\int\limits_{1}^{2}{f\left( x \right)\text{d}x}=10+1=11.$
Đáp án B.