Mathematics

# Find :$\int { 2{ sin }^{ 3 } } \left( { x }\right) cos\left( { x }\right) dx$

##### SOLUTION
$\displaystyle\int{2{\sin}^{3}{x}\cos{x}dx}$
$=2\displaystyle\int{{\sin}^{3}{x}\cos{x}dx}$
Let $t=\sin{x}\Rightarrow dt=\cos{x}dx$
$=2\displaystyle\int{{t}^{3}dt}$
$=2\left[\dfrac{{t}^{4}}{4}\right]+c$ where $c$ is the constant of integration.
$=\left[\dfrac{{\sin}^{4}{x}}{2}\right]+c$ where $t=\sin{x}$

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

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