Google
Câu hỏi: Cho $\int_{0}^{1}{f\left( x \right)\text{d}x}=2$ và $\int_{1}^{4}{f\left( x \right)\text{d}x}=-5$. Tích phân $\int_{0}^{4}{2f\left( x \right)\text{d}x}$ bằng
A. $-3$.
B. $3$.
C. $6$.
D. $-6$.
A. $-3$.
B. $3$.
C. $6$.
D. $-6$.
Ta có
$\int_{0}^{4}{2f\left( x \right)\text{d}x}=2\int_{0}^{4}{f\left( x \right)\text{d}x}=2\left[ \int_{0}^{1}{f\left( x \right)\text{d}x+\int_{1}^{4}{f\left( x \right)\text{d}x}} \right]=2\left( 2-5 \right)=-6.$
Vậy $\int_{0}^{4}{2f\left( x \right)\text{d}x}=-6$.
$\int_{0}^{4}{2f\left( x \right)\text{d}x}=2\int_{0}^{4}{f\left( x \right)\text{d}x}=2\left[ \int_{0}^{1}{f\left( x \right)\text{d}x+\int_{1}^{4}{f\left( x \right)\text{d}x}} \right]=2\left( 2-5 \right)=-6.$
Vậy $\int_{0}^{4}{2f\left( x \right)\text{d}x}=-6$.
Đáp án D.