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Integral problem.

  1. Dec 9, 2009 #1
    I have a problem with this integral. By the way, it's not my homework:)

    [tex]\int\limits_{0}^{+\infty}(\lim\limits_{n\rightarrow+\infty} \displaystyle\frac{1+\cos\frac{x}{n}+\cos\frac{2x}{n}+\ldots+\cos \frac{(n-1)x}{n}}{n} \right))dx[/tex]
     
  2. jcsd
  3. Dec 9, 2009 #2
    The limit inside the integrand can be writen as an integral. If you compute that integral, you find that it is equal to sin(x)/x. If you integrate that from zero to infinity, you get pi/2.
     
  4. Dec 9, 2009 #3
    Hm, but how to compute this integral inside? Why is it equal to sinx/x? I cannot see the way...

    Step by step, please:)
     
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