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Re: Problems with NIntegrate

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  • Subject: [mg1692] Re: [mg1645] Problems with NIntegrate
  • From: John Fultz <jfultz>
  • Date: Mon, 17 Jul 1995 02:14:24 -0400

> HI,
> 	I have come up against a problem in Mathematica I hope someone
> 	in this group may be able to explain to me.
> 	I have defined a function as follows;
> 	fp[p_]=Sqrt[(x^2-1)/(p^2-x^2)]
> 	which I wish to integrate numerically. This I can do with
> 	integer values of p:
> 	NIntegrate[fp[6],{x,1,6}]
> 	= 5.69279
> 	However, if I set p as a real value, such as:
> 	NIntegrate[fp[6.2],{x,1,6.2}]
> 	I get an inexact arithmetic error, and no answer.
> 	Does anybody know why this is happening, and if it's possible
> 	to repair ?
> 	If the problem was caused by the singularity a x=p then surely
> 	this would effect both integer and real values of p.
> 	I have consulted the manual, but if the answer is in there I can't
> 	find it !
> 	Any help would be gratefully received.
> 	Thanks in advance Ian.
> -- 
> --------------------- Ian.Barringer at -----------------
> If you are not entirely satisfied with the contents of this mail,
> please return the complete item to the above address, stating when
> and where it was received, and I will be delighted to send you a
>                               new one.

It *would* affect both integer and real values of p identically, if it
weren't for those tiny little errors computers are always prone to making
in the last digit of machine precision calculations.  I was able to get
your answer to calculate on my machine with:

In[24]:= NIntegrate[fp[6.2], {x, 1, 6.2 - 2 $MachineEpsilon}]

Out[24]= 5.90009

In[25]:= $MachineEpsilon

Out[25]= 2.22045 10

John Fultz
Wolfram Research

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