​Nếu ∫4−1[5f(x)−3]dx=5 thì ∫4−1f(x)dx bằng ​

Question

Nếu \(\int _{-1}^{4}\left[5f\left(x\right)-3\right]dx =5 \)thì \(\int _{-1}^{4}f\left(x\right)dx\)  bằng

A. 4.

B. 3.

C. 2.

D. \(\frac{14}{5} .\)
 

Answer 1

Chọn A

Ta có: \(\int _{-1}^{4}\left[5f\left(x\right)-3\right]dx =5\int _{-1}^{4}f\left(x\right)dx -\left. 3x\right|_{-1}^{4} =5\int _{-1}^{4}f\left(x\right)dx -15\)
\(\Rightarrow \int _{-1}^{4}\left[5f\left(x\right)-3\right]dx =5\Leftrightarrow 5\int _{-1}^{4}f\left(x\right)dx -15=5\Leftrightarrow \int _{-1}^{4}f\left(x\right)dx =4\)