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Câu hỏi: Cho $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-1$, $\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=5$. Tính $\int\limits_{1}^{3}{f\left( x \right)\text{d}x}$
A. 1.
B. 4.
C. 6.
D. 5.
A. 1.
B. 4.
C. 6.
D. 5.
Ta có:
$\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=\int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{1}^{3}{f\left( x \right)\text{d}x}$ $\Leftrightarrow \int\limits_{1}^{3}{f\left( x \right)\text{d}x}=\int\limits_{0}^{3}{f\left( x \right)\text{d}x}-\int\limits_{0}^{1}{f\left( x \right)\text{d}x}\Leftrightarrow \int\limits_{1}^{3}{f\left( x \right)\text{d}x}=5+1=6$
$\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=\int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{1}^{3}{f\left( x \right)\text{d}x}$ $\Leftrightarrow \int\limits_{1}^{3}{f\left( x \right)\text{d}x}=\int\limits_{0}^{3}{f\left( x \right)\text{d}x}-\int\limits_{0}^{1}{f\left( x \right)\text{d}x}\Leftrightarrow \int\limits_{1}^{3}{f\left( x \right)\text{d}x}=5+1=6$
Đáp án C.