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Câu hỏi: Nếu $\int\limits_{1}^{3}{f\left( x \right)dx}=5,\int\limits_{3}^{5}{f\left( x \right)dx}=-2$ thì $\int\limits_{1}^{5}{\left[ f\left( x \right)+1 \right]dx}$ bằng
A. $6.$
B. $-1.$
C. $8.$
D. $7.$
Ta có: $\int\limits_{1}^{5}{f\left( x \right)dx=}\int\limits_{1}^{3}{f\left( x \right)dx}\text{ + }\int\limits_{3}^{5}{f\left( x \right)dx}=5+\left( -2 \right)=3$
Vậy $\int\limits_{1}^{5}{\left[ f\left( x \right)+1 \right]dx}=\int\limits_{1}^{5}{f\left( x \right)}dx+\int\limits_{1}^{5}{dx}=3+\left. x \right|_{1}^{5}=3+5-1=7$
A. $6.$
B. $-1.$
C. $8.$
D. $7.$
Ta có: $\int\limits_{1}^{5}{f\left( x \right)dx=}\int\limits_{1}^{3}{f\left( x \right)dx}\text{ + }\int\limits_{3}^{5}{f\left( x \right)dx}=5+\left( -2 \right)=3$
Vậy $\int\limits_{1}^{5}{\left[ f\left( x \right)+1 \right]dx}=\int\limits_{1}^{5}{f\left( x \right)}dx+\int\limits_{1}^{5}{dx}=3+\left. x \right|_{1}^{5}=3+5-1=7$
Đáp án D.