Mathematics

# $\int { sin\frac { x }{ 2 } } cos\frac { x }{ 2 } dx$

##### SOLUTION
$\displaystyle\int{\sin{\dfrac{x}{2}}\cos{\dfrac{x}{2}}dx}$

$=\dfrac{1}{2}\displaystyle\int{2\sin{\dfrac{x}{2}}\cos{\dfrac{x}{2}}dx}$

$=\dfrac{1}{2}\displaystyle\int{\sin{x}dx}$ since $\sin{2x}=2\sin{x}\cos{x}$

$=\dfrac{1}{2}\left(-\cos{x}\right)+c$

$=\dfrac{-\cos{x}}{2}+c$

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

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