Mathematics

Evaluate:
$$\displaystyle\int\limits_{-1}^{1}\sin^{2015}x.\cos^{2014}x\ dx$$.


SOLUTION
We have the function $$f(x)=\sin^{2015}x.\cos^{2014}x$$ is an odd function.
As $$f(-x)=-f(x) \forall x$$.
So,
$$\displaystyle\int\limits_{-1}^{1}\sin^{2015}x.\cos^{2014}x\ dx=0$$. [ Using the property of definite integral].
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Subjective Medium Published on 17th 09, 2020
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