Groups > comp.soft-sys.math.mathematica > #2266

Numerical/analytical integration around a pole

From	"A. Lapraitis" <ffcitatos@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Numerical/analytical integration around a pole
Date	2011-05-10 12:31 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<iqbb7i$jlt$1@smc.vnet.net> (permalink)

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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

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Numerical/analytical integration around a pole "A. Lapraitis" <ffcitatos@gmail.com> - 2011-05-10 12:31 +0000
  Re: Numerical/analytical integration around a pole Gary Wardall <gwardall@gmail.com> - 2011-05-11 08:26 +0000

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