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Câu hỏi: Cho hàm số $f\left( x \right)$ liên tục trên đoạn $\left[ 0;9 \right]$ thỏa mãn $\int\limits_{0}^{9}{f\left( x \right)\text{d}x}=10$ và $\int\limits_{1}^{3}{f\left( x \right)\text{d}x}=7$. Giá trị $\int\limits_{0}^{3}{f\left( x \right)\text{d}x}+\int\limits_{1}^{9}{f\left( x \right)\text{d}x}$ bằng
A. $-3$.
B. $3$.
C. $17$.
D. $7$.
A. $-3$.
B. $3$.
C. $17$.
D. $7$.
Ta có $\int\limits_{0}^{3}{f\left( x \right)\text{d}x}+\int\limits_{1}^{9}{f\left( x \right)\text{d}x}=\int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{1}^{3}{f\left( x \right)\text{d}x}+\int\limits_{0}^{9}{f\left( x \right)\text{d}x}-\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$
$=\int\limits_{1}^{3}{f\left( x \right)\text{d}x}+\int\limits_{0}^{9}{f\left( x \right)\text{d}x}=7+10=17$.
$=\int\limits_{1}^{3}{f\left( x \right)\text{d}x}+\int\limits_{0}^{9}{f\left( x \right)\text{d}x}=7+10=17$.
Đáp án C.