Cho hàm số f(x)  liên tục trên...

D

- Hướng dẫn giải

Đáp án D

đặt

$\begin{array}{l}t=2x\Rightarrow \frac{1}{2}\underset{\frac{1}{3}}{\overset{1}{\int }}f\left(t\right)dt=13\\ \iff \underset{\frac{1}{3}}{\overset{1}{\int }}f\left(t\right)dt=26\Rightarrow \underset{\frac{1}{3}}{\overset{1}{\int }}f\left(x\right)dx=26\end{array}$

Xét $I=\underset{0}{\overset{1}{\int }}{x}^{2}f\left(x^3\right)dx$ . đặt $u=x^3\Rightarrow du=3x^{2}dx$

$\begin{array}{l}\Rightarrow I=\frac{1}{3}\underset{0}{\overset{1}{\int }}f\left(u\right)du=\\ \frac{1}{3}\underset{0}{\overset{1}{\int }}f\left(x\right)dx=\frac{1}{3}\left[\underset{0}{\overset{\frac{1}{3}}{\int }}f\left(x\right)dx+\underset{\frac{1}{3}}{\overset{0}{\int }}f\left(x\right)dx\right]\\ =\frac{1}{3}\left(1+26\right)=9\end{array}$