Question

` ∫   sin x  \sqrt (1-cos 2x)    dx `

 

Answer 1

` ∫   sin x  .  \sqrt (1-cos 2x)    dx `

` ∫   sin x  \sqrt (2 sin^2 x )    dx `   `[∴ 1 - cos 2A = 2 sin^2 A]`

` =  \sqrt2    ∫   sin^2 x    dx `
\[ = \sqrt{2}\int\left( \frac{1 - \cos 2x}{2} \right)dx\]
\[ = \frac{1}{\sqrt{2}}\int\left( 1 - \cos 2x \right)dx\]
\[ = \frac{1}{\sqrt{2}}\left[ x - \frac{\sin 2x}{2} \right] + C\]