Sunday, 31 August 2014

calculus - How to integrate cos2x?





It seems like I am stuck on such a simple problem:



How to I find the antiderivative of cos2x?
I have tried partial integration, it doesn't seem to work (for me). Some help on how to integrate it would be nice.


Answer




You use the identity (e.g. solving from cos(2x)=2cos2x1):
cos2x=1+cos(2x)2






Addendum: the previous hint will give you the easiest solution, but you mentioned an attempt with integration by parts - that would work too:
cos2xdx=cosxdsinx=cosxsinxsinxdcosx=cosxsinx+sin2xdx=cosxsinx+1cos2xdx=cosxsinx+xcos2xdx2cos2xdx=cosxsinx+x+C

Then you divide by 2.


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