Ta có:[TEX]
\left\{\begin{matrix}du=2x.f’(x^2)dx \\v=\frac{x^2}{2} \end{matrix}\right.[/TEX]
[TEX]\Rightarrow
\left\{\begin{matrix}u=f(x^2) \\dv=xdx \end{matrix}\right.[/TEX]
[TEX]\rightarrow \int_0^1x^3f’(x^2)dx=\frac{x^2}{2}f(x^2)|_0^1-\int_0^1xf(x^2)dx[/TEX]
[TEX]=\frac{1}{2}.f(1)-\int_0^1xf(x^2)dx[/TEX](1)
Đặt [TEX]t=x^2[/TEX]
[TEX]\Rightarrow dt=2xdx[/TEX]
[TEX]\int_0^1xf(x^2)dx=\int_0^1\frac{1}{2}f(t)dt[/TEX][TEX]=\frac{1}{2}\int_0^1f(x)dx=\frac{3}{2}[/TEX]
[TEX](1) \Leftrightarrow \int_0^1x^3f’(x^2)dx=\frac{1}{2}.4-\frac{3}{2}=\frac{1}{2}[/TEX]
Chọn C
có chỗ nào không hiểu bạn hỏi lại nha