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Câu hỏi: Cho hai hàm số $f\left( x \right)$ và $F\left( x \right)$ liên tục trên $\mathbb{R}$ thỏa mãn ${F}'\left( x \right)=f\left( x \right),\forall x\in \mathbb{R}$. Nếu $F\left( 0 \right)=2,F\left( 1 \right)=9$ thì $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$ bằng
A. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-7$.
B. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=7$.
C. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-11$.
D. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=11$.
A. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-7$.
B. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=7$.
C. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-11$.
D. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=11$.
Ta có ${F}'\left( x \right)=f\left( x \right),\forall x\in \mathbb{R}\Rightarrow F\left( x \right)$ là một nguyên hàm của hàm số $f\left( x \right)$.
Ta có $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\left. F\left( x \right) \right|_{0}^{1}=F\left( 1 \right)-F\left( 0 \right)=9-2=7$.
Ta có $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\left. F\left( x \right) \right|_{0}^{1}=F\left( 1 \right)-F\left( 0 \right)=9-2=7$.
Đáp án B.