Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\int\limits_0^1 {{x^3}f'\left( x \right)dx} = - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\
\left\{ \begin{array}{l}
u = {x^3}\\
v' = f'\left( x \right)
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
u' = 3.{x^2}\\
v = f\left( x \right)
\end{array} \right.\\
\left( 1 \right) \Leftrightarrow \mathop {\left. {{x^3}.f\left( x \right)} \right|}\nolimits_0^1 - \int\limits_0^1 {3{x^2}.f\left( x \right)dx} = - 1\\
\Leftrightarrow \mathop {\left. {{x^3}.f\left( x \right)} \right|}\nolimits_0^1 - 3.\int\limits_0^1 {{x^2}.f\left( x \right)dx} = - 1
\end{array}\)
