Mathematics

$$\int { \sin ^{ 2 }{ \cfrac { x }{ 2 }  }  } dx\quad $$


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

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

We know that $$\cos{x}=1-2{\sin}^{2}{\dfrac{x}{2}}$$

$$=\dfrac{1}{2}\displaystyle\int{\left(1-\cos{x}\right)dx}$$

$$=\dfrac{1}{2}\left[x-\sin{x}\right]+c$$

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Subjective Medium Published on 17th 09, 2020
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