anonymous
  • anonymous
integral of (cos(pi*theta))^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jim_thompson5910
  • jim_thompson5910
Hint: Use the identity \[\large \cos^2(x) = \frac{1+\cos(2x)}{2}\]
anonymous
  • anonymous
That's what wolframalpha said too, but I'm wondering whether there's another way to do it. I'm pretty weak on identities...
jim_thompson5910
  • jim_thompson5910
not that I can think of

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jim_thompson5910
  • jim_thompson5910
If you can't remember them, then write them down on a cheat sheet and hopefully your professor will allow you to use one
anonymous
  • anonymous
He's already said that he's not gonna allow a cheat sheet. I thought about quoting Einstein to him, but I don't think it'll help. Guess I'm just going to have to memorize them...
anonymous
  • anonymous
Thanks though.
jim_thompson5910
  • jim_thompson5910
you're welcome
dan815
  • dan815
what was Einsteins quote?
Zarkon
  • Zarkon
you can also do this problem by parts...but you will need to use \(\sin^2(x)+\cos^2(x)=1\)
anonymous
  • anonymous
Einstein's quote was: "[I do not] carry such information in my mind since it is readily available in books. ...The value of a college education is not the learning of many facts but the training of the mind to think."
anonymous
  • anonymous
(I fully agree.)
anonymous
  • anonymous
Zarkon: how would I do that? Replace 1 with sin^2(x) + cos^2(x)?
anonymous
  • anonymous
Move the 1/2 outside of the integral, split them into three parts, and integrate each one separately?
Jhannybean
  • Jhannybean
I really like that quote :) My philosophy on learning works the same way. Haha.
anonymous
  • anonymous
I like it because I have a bad memory. ;)
Zarkon
  • Zarkon
\[\cos^2(u)=\cos(u)\cos(u)\] the use parts
Zarkon
  • Zarkon
then use \[s^2+c^2=1\]
anonymous
  • anonymous
Okay, thanks.
dan815
  • dan815
oh cool nice quote :)
Jhannybean
  • Jhannybean
\[\large \int\limits \cos^2(\theta \pi)d \theta\]if we use @jim_thompson5910 's way: let \(x=(\theta \pi)\) \(dx=d(\theta)\)\[\large \int\limits \frac{1+\cos(2(\pi \theta))}{2}d(\theta)\]\[\large \frac{1}{2}\int\limits (1+\cos(2\pi \theta))d(\theta)\] integrate individually. \[\large \frac{1}{2}[\int\limits d(\theta)+\int\limits \cos(2\pi \theta)d(\theta)]\]

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