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Câu hỏi: Cho $\int\limits_{0}^{3}{f\left( x \right)\text{d}x}=5$ và $\int\limits_{3}^{4}{2f\left( x \right)\text{d}x}=2$ thì $\int\limits_{0}^{4}{f\left( x \right)\text{d}x}$ bằng
A. $10.$
B. $7.$
C. $3.$
D. $6.$
A. $10.$
B. $7.$
C. $3.$
D. $6.$
Theo giả thiết ta có: $\int\limits_{3}^{4}{2f\left( x \right)\text{d}x}=2\Leftrightarrow 2\int\limits_{3}^{4}{f\left( x \right)\text{d}x}=2\Leftrightarrow \int\limits_{3}^{4}{f\left( x \right)\text{d}x}=1.$
Suy ra $\int\limits_{0}^{4}{f\left( x \right)\text{d}x}=\int\limits_{0}^{3}{f\left( x \right)\text{d}x}+\int\limits_{3}^{4}{f\left( x \right)\text{d}x}=5+1=6.$
Suy ra $\int\limits_{0}^{4}{f\left( x \right)\text{d}x}=\int\limits_{0}^{3}{f\left( x \right)\text{d}x}+\int\limits_{3}^{4}{f\left( x \right)\text{d}x}=5+1=6.$
Đáp án D.