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Câu hỏi: Cho các hàm số $f\left( x \right)$ và $F\left( x \right)$ liên tục trên $\mathbb{R}$ thỏa ${F}'\left( x \right)=f\left( x \right),\forall x\in \mathbb{R}.$. Tính $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$
biết $F\left( 0 \right)=2,F\left( 1 \right)=6$.
A. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-4$.
B. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=8$.
C. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-8$.
D. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=4$.
biết $F\left( 0 \right)=2,F\left( 1 \right)=6$.
A. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-4$.
B. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=8$.
C. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=-8$.
D. $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=4$.
Ta có: $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=F\left( 1 \right)-F\left( 0 \right)=4$.
Đáp án D.