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Re: Numerical/analytical integration around a pole

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  Re: Numerical/analytical integration around a pole Murray Eisenberg <murray@math.umass.edu> - 2011-05-11 08:28 +0000

#2292 — Re: Numerical/analytical integration around a pole

With Mathematica 8.0.1 under Windows (32-bit), I get exactly the same 
results from Integrate and NIntegrate here, even when I display 15 
digits in the results from both.


On 5/10/2011 8:31 AM, A. Lapraitis wrote:
> Hello,
>
> I am trying to integrate a 1/(polynomial) function around its pole.
> Could someone explain, why Integrate and NIntegrate give different
> results?
>
> Thanks a lot in advance!
> A. L.
>
>
> In[83]:= y[x_] := .24583 + 0.0175121 x - 0.793943 x^2 + 0.534908 x^3 -
> 0.650198 x^4;
>
> (* Locating the pole *)
> In[86]:= FindRoot[y[x] == 0, {x, .6}]
> Out[86]= {x ->  0.601945}
>
> In[84]:= Integrate[1/(y[x] + I/1000), {x, .5, .7}]
> Out[84]= 5.25406 - 15.0137 I
>
> In[85]:= NIntegrate[1/(y[x] + I/1000), {x, .5, .7}]
> Out[85]= 0.323456 - 3.37701 I
>

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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