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Câu hỏi: Cho hàm số $f\left( x \right)$ liên tục trên $\left[ 0 ; 10 \right]$ thỏa mãn $\int\limits_{0}^{10}{f\left( x \right) \text{d}x}=7$, $\int\limits_{2}^{6}{f\left( x \right) \text{d}x}=3$. 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. $P=4$.
B. $P=-4$.
C. $P=5$.
D. $P=7$.
Ta có: $\int\limits_{0}^{10}{f\left( x \right) \text{d}x}=\int\limits_{0}^{2}{f\left( x \right) \text{d}x}+\int\limits_{2}^{6}{f\left( x \right) \text{d}x}+\int\limits_{6}^{10}{f\left( x \right) \text{d}x}$
$\Rightarrow \int\limits_{0}^{2}{f\left( x \right) \text{d}x}+\int\limits_{6}^{10}{f\left( x \right) \text{d}x}=\int\limits_{0}^{10}{f\left( x \right) \text{d}x}-\int\limits_{2}^{6}{f\left( x \right) \text{d}x}=4$.
A. $P=4$.
B. $P=-4$.
C. $P=5$.
D. $P=7$.
Ta có: $\int\limits_{0}^{10}{f\left( x \right) \text{d}x}=\int\limits_{0}^{2}{f\left( x \right) \text{d}x}+\int\limits_{2}^{6}{f\left( x \right) \text{d}x}+\int\limits_{6}^{10}{f\left( x \right) \text{d}x}$
$\Rightarrow \int\limits_{0}^{2}{f\left( x \right) \text{d}x}+\int\limits_{6}^{10}{f\left( x \right) \text{d}x}=\int\limits_{0}^{10}{f\left( x \right) \text{d}x}-\int\limits_{2}^{6}{f\left( x \right) \text{d}x}=4$.
Đáp án A.