Question

What is ${\int }_{-1}^{1}x\left|x\right|dx$ equal to?

• A. $2$
• B. $1$
• C. $0$
• D. $-1$

Answer 1

The correct option is C $0$

$I={\int }_{-1}^{1}x\left|x\right|dx$

$=-{\int }_{-1}^0{x}^{2}dx+{\int }_0^1{x}^{2}dx$

$=\frac{-1}{3}{\left[x^3\right]}_{-1}^0+\frac{1}{3}{\left[x^3\right]}_0^1=-\frac{1}{3}+\frac{1}{3}=0$

Hence, C is correct.