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How to integrate this? quick question

  1. Oct 29, 2006 #1
    [tex] \int_{0}^{2 \lambda} \cos({\frac{kx}{2}}) \cos({nx}) dx[/tex]

    I can't find my calc2 notes and it's killing me! This thing came up half way through the computation of the fourier series of [tex]f(x) = A\cos({\frac{\pi x}{\lambda}})[/tex]..and i can't remember how to do it!

    I am very aware of the trig identity below, but i would prefer not to use it for obvious reasons.

    [tex]\cos{\alpha}\cos{\beta} = \frac{1}{2}[\cos{\frac{(\alpha + \beta)}{2} + \cos{\frac{(\alpha - \beta)}{2}][/tex]

    I have the exact same question except instead of two cosines there's one cosine and one sine..any help is appreciated!
     
    Last edited: Oct 29, 2006
  2. jcsd
  3. Oct 30, 2006 #2

    HallsofIvy

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    What are the obvious reasons? I would think that using that identity would be the "obvious" way to do it!

    (Your identity is wrong: there is no 1/2 inside the functions. It is
    [tex]\cos{\alpha}\cos{\beta} = \frac{1}{2}[\cos(\alpha + \beta) + \cos{(\alpha - \beta)][/tex])

    And
    [tex]sin(\alpha)cos(\beta)= \frac{1}{2}[sin(\alpha+ \beta)+ sin(\alpha-\beta)][/tex]
     
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