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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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