Question

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

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

Answer 1

Answer: (C)

$0$

Let $f\left(x\right)=x|x|$.

Now, $f(-x)=-x|x|=-f\left(x\right)$.

So the function $f\left(x\right)$ is an odd function.

So,

$\underset{-1}{\overset{1}{\int }}x|x|dx=0$. [ Using the property of definite integral]