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May 4th, 2013, 01:12 PM   #1
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Computation of an integral.

This problem was encountered here.

Subject: computation of the integral .

We will integrate the function (0<p<1) over the next figure.


Letting and using the inequality

so . Since as , . So as we are left with,

and since the last two integrals converge absolutely we can omit the P.V. (principal value) and knowing that we get


So and for p=1/3 we get .
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