Tìm hàm số y=f(x) biết rằng f(x) = ({x^2} - x)(x + 1) và f(0)=3

* Hướng dẫn giải

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\left\{ {\begin{array}{*{20}{l}}
{f(x) = \int {({x^2} - x)(x + 1)dx} }\\
{f(0) = 3}
\end{array}} \right.\\
 \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{f(x) = \int {({x^3} - x)dx} }\\
{f(0) = 3}
\end{array}} \right.
\end{array}\\
\begin{array}{l}
 \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{f(x) = \frac{{{x^4}}}{4} - \frac{{{x^2}}}{2} + C}\\
{f(0) = C = 3}
\end{array}} \right.\\
 \Rightarrow f(x) = \frac{{{x^4}}}{4} - \frac{{{x^2}}}{2} + 3.
\end{array}
\end{array}\)