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Câu hỏi: Cho hàm số $f\left( x \right)$ có đạo hàm trên đoạn $\left[ -1;4 \right]$, $f\left( 4 \right)=2021$, $\int\limits_{-1}^{4}{{f}'\left( x \right)\text{d}x}=2020$. Tính $f\left( -1 \right)$ ?
A. $f\left( -1 \right)=-1$.
B. $f\left( -1 \right)=1$.
C. $f\left( -1 \right)=3$.
D. $f\left( -1 \right)=2$.
A. $f\left( -1 \right)=-1$.
B. $f\left( -1 \right)=1$.
C. $f\left( -1 \right)=3$.
D. $f\left( -1 \right)=2$.
Ta có $\int\limits_{-1}^{4}{{f}'\left( x \right)\text{d}x}=\left. f\left( x \right) \right|_{-1}^{4}$ $=f\left( 4 \right)-f\left( -1 \right)$ $\Rightarrow f\left( -1 \right)=f\left( 4 \right)-\int\limits_{-1}^{4}{{f}'\left( x \right)\text{d}x}$
$=2021-2020=1$.
$=2021-2020=1$.
Đáp án B.