Integral problem.

  • Thread starter Upiór
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  • #1
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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]
 

Answers and Replies

  • #2
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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.
 
  • #3
2
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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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