|x|^3 dx is equal to: - Vidyadip

MCQ

$\int|\text{x}|^3\text{ dx}$ is equal to:

A
$\frac{-\text{x}^4}{4}+\text{C}$
B
$\frac{|\text{x}|^4}{4}+\text{C}$
C
$\frac{\text{x}^4}{4}+\text{C}$
✓
none of these.

✓

Answer

Correct option: D.

none of these.

$\int|\text{x}|^3\text{ dx}$
$|\text{x}|=\begin{cases}\text{x},\text{ x}\geq0\\-\text{x},\text{ x}<0\end{cases}$
Case $I:$
When $\text{x}\geq0$
$\therefore\ \int|\text{x}|^3\text{ dx}$
$=\int\text{x}^3\text{ dx}$
$=\frac{\text{x}^4}{4}+\text{C}$
Case $II:$
$\text{x}<0$
$\int|\text{x}|^3\text{ dx}$
$=-\int\text{x}^3\text{ dx}$
$=\frac{-\text{x}^4}{4}+\text{C}$

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