Integration of some function containing a singularity

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Xianjie
Xianjie 2012-3-20
Dear All,
These days I am working on some integration integrate(cos(x)*sin(x)/x^t),x(0,a),a is a value. the value fot t is 1, 2, 3. The function also have the form cosx*cosx and sinx*sinx. The value x = 0 is the singularity. How to overcome this singularity. The function quadgk can integrate some funtion with endpoint singularity. x = 0 is the end point singularity. But the integral is not correct when use quadgk. How to solve this problem.
Thank you for your concern.

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Mike Hosea
Mike Hosea 2012-3-20
QUADGK has no trouble when t=1, but for t=2,3,4,... the correct answer, if I am not mistaken, is Inf. You were expecting QUADGK to return Inf for you?
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Xianjie
Xianjie 2012-3-21
But when the x=0 is not selected, choose x=0.001, the integration is ok. How about this phenomenon. Is there some numerical evaluate the results? I calculate the strain energy of circular plate. x=0 is the center of circular plate.
Thanks
Mike Hosea
Mike Hosea 2012-3-21
I believe QUADGK handles that case properly, though you may well run into precision issues.

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