Mathematics

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

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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$\int \frac{2x^{2}}{3x^{4}2x} dx$