Mathematics

# Evaluate:$\int { \sqrt { \cfrac { 1-\cos { 2x } }{ 2 } } } dx$

##### SOLUTION
Given $\displaystyle\int{\sqrt{\dfrac{1-\cos{2x}}{2}}dx}$

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

$=\dfrac{1}{\sqrt{2}}\displaystyle\int{\sqrt{1-\left(1-2{\sin}^{2}{x}\right)}dx}$    $[\because \cos 2x=1-2\sin^2 x]$

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

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

$=\displaystyle\int{\sin{x}dx}$

$=-\cos{x}+c$

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

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