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Question

Find the value of $$n$$ such that $$\displaystyle\int\limits_{-2}^{2} x^n  \ dx=0.$$


Solution

We've, $$\displaystyle\int\limits_{-2}^{2} f(x)  \ dx=0$$ for $$f(x)$$ being odd function.
Now $$x^n$$ will be an odd function for $$n$$ being odd integral value.
So, if $$n$$ is odd integer number then $$\displaystyle\int\limits_{-2}^{2} x^n  \ dx=0$$ will hold.

Mathematics

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