Mathematics

$$\displaystyle \int {\sin x\sqrt {1 - \cos 2x} } \;dx$$


SOLUTION
$$\displaystyle \int sin\,x\sqrt{1-cos\,2x}\,\,dx\,\, 1-cos\,x = 2\,sin^{2}x $$
$$\displaystyle \Rightarrow \sqrt{2}\int sin\,x(sin\,x)dx $$
$$\displaystyle \Rightarrow \sqrt{2}\int sin^{2}x\,dx \Rightarrow \frac{+\sqrt{2}}{2}\int 1-cos\,2x\,dx $$
$$\displaystyle \frac{1}{\sqrt{2}}(x)-\frac{1}{2\sqrt{2}}sin\,2x $$ 
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Subjective Medium Published on 17th 09, 2020
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