Question

find the auti derivatives of
S sin^2 x dx​

Answer 1

Step-by-step explanation:

We have,

$\int \sin^{2} (x) dx$

$= \int \frac{1 - \cos(2x) }{2} dx$

$= \int \bigg( \frac{1}{2} - \frac{ \cos(2x) }{2} \bigg) dx$

$= \int \frac{1}{2}dx - \int\frac{ \cos(2x) }{2} dx$

$= \frac{1}{2} \int \: dx - \frac{1}{2} \int \cos(2x) dx$

$= \frac{1}{2} x + \frac{c _{1} }{2} - \frac{1}{4} \sin(2x) + c_{2}$

$= \frac{x}{2} - \frac{1}{4} \sin(2x) + C$

Where, C is a constant