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Homework Help: Indefinite integral

  1. Feb 1, 2005 #1

    ProBasket

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    [tex]\int sin(9x)sin(16x)dx[/tex]

    is there another way of solving the problem above besides using the multiple angles formula?
     
    ProBasket, Feb 1, 2005
  2. jcsd
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  3. Feb 1, 2005 #2

    vincentchan

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    use this identity:

    [tex]
    sin u = \frac{e^{iu}-e^{-iu}}{2i}
    [/tex]

    edit:
    expand the sine in term of exponential, multiply them and regroup them into 2 cosine, then do the integral
     
    Last edited: Feb 1, 2005
    vincentchan, Feb 1, 2005
  4. Feb 1, 2005 #3

    ProBasket

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    wow looks more difficult than using multiple angles formula. i just thought there's an easier way to do it so i wont have to remeber crazy amount of formulas when it's test day.
     
    ProBasket, Feb 1, 2005
  5. Feb 1, 2005 #4

    ehild

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    Homework Helper

    use

    [tex] \sin{\alpha}\sin{\beta} = \frac{\cos(\alpha-\beta) - \cos(\alpha + \beta)}{2}[/tex]

    ehild
     
    ehild, Feb 1, 2005
  6. Feb 1, 2005 #5

    vincentchan

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    actually, my way is much much much more easier than remember you formulas.....
    I can eye ball the answer using my way......
    the answer is....
    1/14 sin7x - 1/50 sin25x
    the expansion of the complex number is easy.... there are only 4 terms
     
    vincentchan, Feb 1, 2005
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