How to integrate a sinc function?

  • Thread starter yungman
  • Start date
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Can anyone show me how to do this:

[tex]\int_a^b \left[\frac {\sin x}{x}\right]^2 dx [/tex]
 
It depends on you purpose, but in general the best bet may be power series methods.

The Taylor series for sin2 is

[itex]\sin^2 x = -\sum^\infty_{k=1} \frac{(-1)^{k} 2^{2k-1}x^{2k}}{(2k)!}[/itex]

So we have

[itex]\frac{\sin^2 x}{x^2} = -\sum^\infty_{k=1} \frac{(-1)^{k} 2^{2k-1}x^{2k-2}}{(2k)!}[/itex]

Then you can try term-wise integration and the fundamental theorem of calculus to get a general form for the answer as a power series.
 

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