Wednesday, 30 August 2017

integration - how to calculate the integral of sin2(x)/x2











sin2(x)/x2=π according to wolfram alpha. That is such a beautiful result! But how do I calculate this integral by hand?



Thanks in advance.


Answer



The answer may be found by using complex analysis, specifically the residue theorem. A full deriviation may be found here.



I know of an easy way to derive this result using real analysis alone.


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