Mathematics

# Evaluate $\int { \sin ^{ 3 }{ x } } \sin { 2x } \, dx$.

##### SOLUTION
$\displaystyle\int{{\sin}^{3}{x}\sin{2x}dx}$
$=\displaystyle\int{{\sin}^{3}{x}2\sin{x}\cos{x}dx}$
$I=2\displaystyle\int{{\sin}^{4}{x}\cos{x}dx}$

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

$I=2\displaystyle\int{{t}^{4}dt}$

$=2\left(\dfrac{{t}^{5}}{5}\right)+c$ , where $c$ is the constant of integration

$=\dfrac{2 \, {\sin}^{5}{x}}{5}+c$ , where $t=\sin{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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