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Câu hỏi: Cho $\int\limits_{-2}^{2}{f\left( x \right)\text{d}x}=1$, $\int\limits_{-2}^{4}{f\left( t \right)\text{d}t}=-4$. Tính $\int\limits_{2}^{4}{f\left( y \right)\text{d}y}$.
A. $I=5$.
B. $I=-3$.
C. $I=3$.
D. $I=-5$.
A. $I=5$.
B. $I=-3$.
C. $I=3$.
D. $I=-5$.
Ta có: $\int\limits_{-2}^{4}{f\left( t \right)\text{d}t}=\int\limits_{-2}^{4}{f\left( x \right)\text{d}x}$, $\int\limits_{2}^{4}{f\left( y \right)\text{d}y}=\int\limits_{2}^{4}{f\left( x \right)\text{d}x}$.
Khi đó: $\int\limits_{-2}^{2}{f\left( x \right)\text{d}x}+\int\limits_{2}^{4}{f\left( x \right)\text{d}x}=\int\limits_{-2}^{4}{f\left( x \right)\text{d}x}$.
$\Rightarrow \int\limits_{2}^{4}{f\left( x \right)\text{d}x}=\int\limits_{-2}^{4}{f\left( x \right)\text{d}x}-\int\limits_{-2}^{2}{f\left( x \right)\text{d}x}=-4-1=-5$.
Vậy $\int\limits_{2}^{4}{f\left( y \right)\text{d}y}=-5$.
Khi đó: $\int\limits_{-2}^{2}{f\left( x \right)\text{d}x}+\int\limits_{2}^{4}{f\left( x \right)\text{d}x}=\int\limits_{-2}^{4}{f\left( x \right)\text{d}x}$.
$\Rightarrow \int\limits_{2}^{4}{f\left( x \right)\text{d}x}=\int\limits_{-2}^{4}{f\left( x \right)\text{d}x}-\int\limits_{-2}^{2}{f\left( x \right)\text{d}x}=-4-1=-5$.
Vậy $\int\limits_{2}^{4}{f\left( y \right)\text{d}y}=-5$.
Đáp án D.