Mathematics

$$\int { \sin ^{ 2 }{ b }  } xdx\quad \quad $$


SOLUTION
$$\displaystyle\int{{\sin}^{2}{bx}dx}$$

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

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

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

$$=\dfrac{x}{2}-\dfrac{\sin{2bx}}{4b}+c$$
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Subjective Medium Published on 17th 09, 2020
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