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Câu hỏi: Cho hàm số $f\left( x \right)$ liên tục trên đoạn $\left[ 0; 10 \right]$ và $\int\limits_{0}^{10}{f\left( x \right)\text{d}x=7}$ và $\int\limits_{2}^{6}{f\left( x \right)\text{d}x=3}$. Tính $P=\int\limits_{0}^{2}{f\left( x \right)\text{d}x+\int\limits_{6}^{10}{f\left( x \right)\text{d}x}}$.
A. $P=7$.
B. $P=-4$.
C. $P=4$.
D. $P=10$.
A. $P=7$.
B. $P=-4$.
C. $P=4$.
D. $P=10$.
Ta có $\int\limits_{0}^{10}{f\left( x \right)\text{d}x=7}$ $\Leftrightarrow \int\limits_{0}^{2}{f\left( x \right)\text{d}x}+\int\limits_{2}^{6}{f\left( x \right)\text{d}x}+\int\limits_{6}^{10}{f\left( x \right)\text{d}x}=7$
$\Leftrightarrow \int\limits_{0}^{2}{f\left( x \right)\text{d}x}+\int\limits_{6}^{10}{f\left( x \right)\text{d}x}=7-3=4$.
Vậy $P=4$.
$\Leftrightarrow \int\limits_{0}^{2}{f\left( x \right)\text{d}x}+\int\limits_{6}^{10}{f\left( x \right)\text{d}x}=7-3=4$.
Vậy $P=4$.
Đáp án C.