Integrating the function sqrt(1-sin2x)

[rwx1606]

Homework Statement

Integrate the following $$\int$$$$\sqrt{1-sin2x}$$ dx

Homework Equations

sin2x=2cosxsinx
cos2x= cos^2 (x) -sin^2 (x)

The Attempt at a Solution

I've rearranged the integral so its 1-sin2x/$$\sqrt{1-sin2x}$$ but other than that I've just been randomly trying stuff. Any hints on where to begin?

 

[rocomath]

Try using the fact that $$\cos^2 x + \sin^2 x =1$$

 

[rwx1606]

still not getting anywhere.i tried multiplying top and bottom by 1-sin2x. And then using what you said I got a cos^2(2x) over an ugly thing.

 

[rocomath]

$$\int\sqrt{\cos^2 x - 2 \sin x \cos x + \sin^2 x}dx$$

Simplify!