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Fourier series and calculate integral

  1. May 27, 2010 #1
    1. The problem statement, all variables and given/known data
    expand the function in Fourier series and calculate the integral
    [tex] f(x)= (sinx)^2(cosx)^3, 2\pi [/tex] is the period
    calculate the integral
    [tex] \int_{0}^{2\pi}f(x)dx[/tex]
    please help......have absolutely no idea how to calculate it....


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 27, 2010 #2

    LCKurtz

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    Express the cos3(x) as (1 - sin2(x))cos(x) and use the substitution u = sin(x).
     
  4. May 27, 2010 #3

    vela

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    Note that f(x) is even, so what does this tell you about its Fourier expansion?

    You can use trig identities to rewrite f(x) as a Fourier series, instead of having to crank out the integrals. In particular, look at the power-reduction formulas, and use what you know about what its Fourier expansion should look like to guide you.

    http://en.wikipedia.org/wiki/List_of_trigonometric_identities
     
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