Thread: Integrating expression by power reduction formula

Hi everyone! So, I have to integrate the expression:

sin²(x/2) dx

in the book it says that it integrates to become:

1/2 - cosx / 2

In order to get there, the power reduction formula is used, I am just not sure how to use the formula when the initial expression is not sin²x?

Thanks for reading

The power-reducing formula,
sin² u = (1 - cos 2u)/2,
can be used in cases other than u = x.

Here you need to replace u, in each instance, with x/2.

This results in the relevant formula to your case,

sin² x/2 = (1 - cos 2(x/2))/2 or
sin² x/2 = (1 - cos x)/2.

Hope this helps.

Thank you so much for the help! I understand completely now,