Cho f( x) liên tục trên

A

- Hướng dẫn giải

Đáp án A.

Xét $\underset{0}{\overset{1}{\int }}f\left(2x\right)=2,$ đặt $2x=t$

$\Rightarrow 2=\underset{0}{\overset{2}{\int }}f\left(t\right)d\left(\frac{t}{2}\right)=\frac{1}{2}\underset{0}{\overset{2}{\int }}f\left(t\right)dt$

$=\frac{1}{2}\underset{0}{\overset{2}{\int }}f\left(x\right)dx\Rightarrow \underset{0}{\overset{2}{\int }}f\left(x\right)dx=4.$

Ta có

$\underset{0}{\overset{2}{\int }}x.f\text{'}\left(x\right)dx=\underset{0}{\overset{2}{\int }}xd\left(f\left(x\right)\right)$

$$\begin{gathered} =x.f\left(x\right)\left|{}_0^2\right.-\underset{0}{\overset{2}{\int }}f\left(x\right)dx=2f\left(2\right) \\ =2.16-4=28. \end{gathered}$$