[TEX]\displaystyle\int_0^1xf’(x)dx+\displaystyle \int_0^1f’(x)=10[/TEX]
[TEX]\Leftrightarrow \displaystyle \int_0^1xf’(x)dx+f(1)-f(0) =10[/TEX] (1)
đặt [TEX]
\left\{\begin{matrix}u=x
\\dv=f’(x)dx
\end{matrix}\right.
[/TEX]
[TEX]\Rightarrow
\left\{\begin{matrix}du=dx
\\v=f(x)
\end{matrix}\right.
[/TEX]
[TEX]\Rightarrow \displaystyle \int_0^1xf’(x)dx=xf(x) \left| \begin{matrix}0\\1 \end{matrix}\right. -\displaystyle \int_0^1f(x)dx[/TEX]
[TEX]=f(1)- \displaystyle\int_0^1f(x)dx[/TEX]
pt (1) [TEX]\Leftrightarrow \displaystyle \int_0^1f(x)dx= 2f(1)-f(0)-10=-8[/TEX]
Chọn D
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