​Cho ∫21[3f(x)−2x]dx=6. Khi đó ∫21f(x)dx bằng ​

Question

Cho \(\int _{1}^{2}\left[3f\left(x\right)-2x\right]dx =6\). Khi đó \(\int _{1}^{2}f\left(x\right) dx\) bằng

A. 1

B. -3

C. 3

D. -1
 

Answer 1

Chọn C. 
\(\begin{array}{l} {\int _{1}^{2}\left[3f\left(x\right)-2x\right]dx =6\Leftrightarrow 3\int _{1}^{2}f\left(x\right)dx-2\int _{1}^{2}xdx  =6\Leftrightarrow 3\int _{1}^{2}f\left(x\right)dx-2. \left. \frac{x^{2} }{2} \right|_{1}^{2} =6} \\ {\Leftrightarrow 3\int _{1}^{2}f\left(x\right)dx=9\Leftrightarrow  \int _{1}^{2}f\left(x\right)dx=3 .} \end{array}\)