Find the antiderivative of cos x + sin x?

QUESTION POSTED AT 16/04/2020 - 06:30 PM

Answered by admin AT 16/04/2020 - 06:30 PM

-1/4 cos 2x + C 

or 1/2 sin^2 x + C 
or -1/2 cos^2 x + C 

well, sinxcosx=sin2x2 so you are looking at12∫ sin2dx=(12)[(12)(−cos2x)+C]=−14cos2x+C'

or maybe easier you can notice the pattern that (sinnx)'=nsinn−1xcosx and pattern match. here n−1=1 so n = 2 so we trial (sin2x)' which gives us 2sinxcosx so we now that the anti deriv is 12sin2x+C

the other pattern also works ie(cosnx)'=ncosn−1x(−sinx)=−ncosn−1xsinx

so trial solution (−cos2x)'=−2cosx(−sinx)=2cosxsinx so the anti deriv is 12cos2x+C

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QUESTION POSTED AT 01/06/2020 - 04:46 PM