Question

The value of $\underset{-1}{\overset{1}{\int }}x|x|dx$ is

• A. $2$
• B. $1$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

$\underset{-1}{\overset{1}{\int }}x|x|dx$
$=\underset{-1}{\overset{0}{\int }}-x^{2}dx+\underset{0}{\overset{1}{\int }}{x}^{2}dx$
$={[-\frac{x^3}{3}]}_{-1}^0+{\left[\frac{x^3}{3}\right]}_0^1=-\frac{1}{3}+\frac{1}{3}=0$