Question

The value of ${\int }_{-1}^{1}x|x|dx$, is equal to

• A. $1$
• B. $\frac{1}{2}$
• C. $0$
• D. none of these

Answer 1

The correct option is C $0$

$I={\int }_{-1}^{1}x|x|dx$
$={\int }_{-1}^{0}x(-x)dx+{\int }_0^{1}x\left(x\right)dx$
$=[-\frac{x^3}{3}{]}_{-1}^0+[\frac{x^3}{3}{]}_0^1$
$I=-\frac{1}{3}+\frac{1}{3}=0$