Mathematics

Evaluate the following integrals:$\int { \sin ^{ 5 }{ x } \cos ^{ }{ x } } dx$

SOLUTION
$I=\displaystyle\int{{\sin}^{5}{x}\cos{x}dx}$

Let

$t=\sin{x}\Rightarrow\,dt=\cos{x}dx$

$I=\displaystyle\int{{t}^{5}\,dt}$

$=\dfrac{1}{6}{t}^{6}+c$ where $c$ is the constant of integration.

$=\dfrac{1}{6}{\sin}^{6}{x}+c$ where $t=\sin{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

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