Integrating the function sqrt(1-sin2x)

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Homework Help Overview

The discussion revolves around integrating the function \(\int\sqrt{1-\sin 2x} \, dx\), which involves trigonometric identities and simplifications related to sine and cosine functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore various manipulations of the integral, including rearranging terms and applying trigonometric identities. Questions arise regarding effective starting points and simplification strategies.

Discussion Status

Some participants have offered hints related to trigonometric identities, while others express difficulty in progressing with their attempts. Multiple approaches are being considered, but no consensus or clear direction has emerged yet.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the types of assistance they can provide to one another.

rwx1606
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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?
 
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Try using the fact that \cos^2 x + \sin^2 x =1
 
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.
 
\int\sqrt{\cos^2 x - 2 \sin x \cos x + \sin^2 x}dx

Simplify!
 

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