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Integration-im lost

  1. Sep 13, 2007 #1
    integration--im lost

    1. The problem statement, all variables and given/known data
    how do you integrate this one

    [tex]\int sint cosnt dt[/tex]

    i tried using this identity 1/2 [sin(t-nt) + sin (t-nt)]

    then i got stuck so i used another identity again
    sin (t[tex]^{+}_{-}nt [/tex])= sintcosnt[tex]^{+}_{-}[/tex]costsinnt

    the result is the original equation..

    to sum it all, im hopelessly stuck
  2. jcsd
  3. Sep 13, 2007 #2
    uhmmm hi!!! i dont really know what to do...and blood is dripping out of my nose!! waaaah!! *dramatic*
  4. Sep 13, 2007 #3


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    A sure fire way that doesn't take a lot of brains is to use identities like cos(x)=(exp(ix)-exp(-ix))/2 (deMoivre). You can convert the whole thing to exponentials and they are easy.
  5. Sep 13, 2007 #4


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    Well, this identity doesn't look right to me.

    Nope, you don't need to expand it. It'll give you the original expression. Hint: Can you simplify: t - nt, and t + nt?
  6. Sep 13, 2007 #5
    1/2 [sin(t+nt) + sin (t-nt)]--->sorry, got it wrong..this ones correct
  7. Sep 13, 2007 #6
    that gives me t[tex]^{2}[/tex]-n[tex]^{2}[/tex]t[tex]^{2}[/tex]

    but where would i plug this equation

    im really not that good at manipulating equation..havent learned trigonometry at heart
  8. Sep 13, 2007 #7


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    Ack. >"< No, that's not correct at all.

    Well, it's not that hard. We have:

    sin(t + nt) = sin[(n + 1)t]. Which can be easily integrated. Simple, eh? :)

    You can do the same to the other one. Can you go from here? :)
  9. Sep 13, 2007 #8
    aw sorrryyy, lol...just being my dumb self again..shame on me.. lol
    thank you very much!
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