Mathematics

Integrate:
$$\int \sin x \sqrt { 1 + \cos 2 x } d x$$


SOLUTION

$$\\\int\>sinx\sqrt{1+(2cos^2x-1)}dx\\=\int\>sinx\times\sqrt{2}\>cosx\>dx\\=\sqrt{2}\int\>sinx\>cosx\>dx\\=(\frac{\sqrt{2}}{2})\int\>sin2x\>dx\\=(\frac{1}{\sqrt{2}})\left[-(\frac{cos2x}{2})\right]+C\\=(\frac{-cos2x}{2\sqrt{2}})+C$$

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Subjective Medium Published on 17th 09, 2020
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