​Nếu ∫21f(x)dx=−3và∫31f(x)dx=1thì∫32f(x)dx bằng ​

Question

Nếu\( \int _{1}^{2}f \left(x\right){\rm d}x=-3 và \int _{1}^{3}f \left(x\right){\rm d}x=1 thì \int _{2}^{3}f \left(x\right){\rm d}x\) bằng

A. 4

B. -4

C. -2

D. -3
 

Answer 1

Chọn A

=Ta có: 
\(\int _{1}^{3}f \left(x\right){\rm d}x=\int _{1}^{2}f \left(x\right){\rm d}x+\int _{2}^{3}f \left(x\right){\rm d}x\)
\(\Leftrightarrow \int _{2}^{3}f \left(x\right){\rm d}x=\int _{1}^{3}f \left(x\right){\rm d}x-\int _{1}^{2}f \left(x\right){\rm d}x\)

\( \Leftrightarrow \int _{2}^{3}f \left(x\right){\rm d}x=1-\left(-3\right)=4.\)