Mathematics

$$\int { sin\frac { x }{ 2 }  } cos\frac { x }{ 2 } dx$$


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

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

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

$$=\dfrac{1}{2}\left(-\cos{x}\right)+c$$ 

$$=\dfrac{-\cos{x}}{2}+c$$
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Subjective Medium Published on 17th 09, 2020
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