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Math Help - inegral with 2 sine fcns

  1. #1
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    inegral with 2 sine fcns

    Hello! I am trying to expand the function f(x)=sin|x| as Fourier series on the interval |x|<\pi
    Since the function is even we can write
    a_{n}=\frac{2}{\pi}\int_{0}^{\pi}sinxcosnxdx

    but here my problem starts. I try to solve this integral as indefinite integral first but I am going in circles....

    \int sinxcosnxdx=\{u=cosnx,\ dv=sinx\}=\<br /> <br />
-cosxcosnx-\frac{1}{n}\int sinnxcosxdx=\{u=sinnx,\ dv=cosx\}=<br /> <br />
-cosxcosnx-\frac{1}{n}[sinnxsinx-\frac{1}{n}\int cosnxcosx]=.......

    Could someone show me how to compute this integral?
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  2. #2
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    Re: inegral with 2 sine fcns

    \sin x \cos nx = 1/2\,\sin \left( x+nx \right) -1/2\,\sin \left( -x+nx \right)
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