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Câu hỏi: Cho $f\left( x \right)$ và $g\left( x \right)$ là các hàm số liên tục trên $\mathbb{R}$, thỏa mãn $\int\limits_{0}^{10}{f\left( x \right)\text{d}x}=21; \int\limits_{0}^{10}{g\left( x \right)\text{d}x}=16; \int\limits_{3}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}=2$. Tính $I=\int\limits_{0}^{3}{\left( f\left( x \right)-\text{g}\left( x \right) \right)\text{d}x}$
A. $I=3$.
B. $I=15$.
C. $I=11$.
D. $I=7$.
A. $I=3$.
B. $I=15$.
C. $I=11$.
D. $I=7$.
Do hàm số liên tục trên $\mathbb{R}$ nên hàm số liên tục trên đoạn $\left[ 0; 10 \right]$.
Ta có $\int\limits_{0}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}=\int\limits_{0}^{3}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}+\int\limits_{3}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}$
$\Rightarrow I=\int\limits_{0}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}-\int\limits_{3}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}=5-2=3$.
Ta có $\int\limits_{0}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}=\int\limits_{0}^{3}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}+\int\limits_{3}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}$
$\Rightarrow I=\int\limits_{0}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}-\int\limits_{3}^{10}{\left( f\left( x \right)-g\left( x \right) \right)\text{d}x}=5-2=3$.
Đáp án A.
