Mathematics

The value of the integral $$\displaystyle\int{\sin{x}{\cos}^{4}{x}dx}$$ where $$x\in\left[-1,\,1\right]$$ is 


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SOLUTION
$$f\left(x\right)=\sin{x}{\cos}^{4}{x},$$

$$f\left(-x\right)=\sin{\left(-x\right)}{\cos}^{4}{\left(-x\right)}=-f\left(x\right)$$

Since $$f\left(x\right)$$ is an odd function, $$\displaystyle\int_{-1}^{1}\sin{x}{\cos}^{4}{x}dx=0$$
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Single Correct Medium Published on 17th 09, 2020
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