Mathematics

$$\displaystyle \overset{1}{\underset{-1}{\int}} x|x|dx$$ is equal to


ANSWER

$$0$$


SOLUTION
Let $$f(x)=x|x|$$.
Now, $$f(-x)=-x|-x|=-x|x|=-f(x)$$.
So we have $$f(x)$$ is an odd function.
Now,
$$\displaystyle\int\limits_{-1}^{1}x|x|\ dx =0$$. [ Using property of definite integral]
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Single Correct Medium Published on 17th 09, 2020
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