Integration of some function containing a singularity
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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
2012-3-20
0 个投票
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?
3 个评论
Walter Roberson
2012-3-20
As a point of interest, could someone run
syms x
syms t positive
int(cos(x)*sin(x)/x^t,x=0..pi)
through MuPAD ?
Maple mis-integrates in this case (which I just reported a moment ago.)
Xianjie
2012-3-21
Mike Hosea
2012-3-21
I believe QUADGK handles that case properly, though you may well run into precision issues.
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