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Integral of trigonometric function

  • Thread starter Ry122
  • Start date
565
2
How do I find the derivative of cos2x?
Do I use the chain rule?
u=2x
u'=2
y=cosu
y'=-sinu
dy/dx=-2sin(2x)
Edit: Sorry. I mean derivative, not integral.
 
Last edited:
That looks good, my friend, so I think you've got it!
 
1,750
1
yes, that's correct

Now try it all in one step!
 
565
2
what about the integral of xsin(x/2).
How would I do that?
 
1,750
1
Integral or Derivative? You might want to write it out properly ...
 
565
2
integral of xsin(x/2) dx
 
1,750
1
[tex]\int x\sin{\frac x 2}dx[/tex]

Try integrating by parts.
 
351
2
use sin(x/2) identity and try to convert everything to sin..

I have a feeling that there's an easier way to do that
 

tiny-tim

Science Advisor
Homework Helper
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How do I find the derivative of cos2x?
Do I use the chain rule?
u=2x
u'=2
y=cosu
y'=-sinu
dy/dx=-2sin(2x)
Edit: Sorry. I mean derivative, not integral.
Hi Ry122! :smile:

You can also use the chain rule without having to define a u:

dcos2x/dx = (dcos2x/d(2x))(d(2x)/dx) = (-sin2x)(2). :smile:

(That way, you can eventually do these things in your head! :wink:)
 

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