Question

\[\int \left| x \right|^3 dx\] is equal to

Options

• \[\frac{- x^4}{4} + C\]

• \[\frac{\left| x \right|^4}{4} + C\]

• \[\frac{x^4}{4} + C\]

• none of these

Answer 1

none of these

\[\int \left| x \right|^3 dx\]
\[\left| x \right| = \begin{cases}x,& x \geq 0\\ - x,& x < 0\end{cases}\]
Case 1 :-
\[\text{When }x \geq 0\]
\[ \therefore \int \left| x \right|^3 dx\]
\[ = \int x^3 dx\]
\[ = \frac{x^4}{4} + C\]
Case 2 :-
\[x < 0\]
\[\int \left| x \right|^3 dx\]
\[ = - \int x^3 dx\]
\[ = \frac{- x^4}{4} + C\]