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Re: Calculate a numerical integral with enough precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114736] Re: Calculate a numerical integral with enough precision
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 14 Dec 2010 06:57:56 -0500 (EST)

You want WorkingPrecision to be at least as large as PrecisionGoal. However, the default is to use a WorkingPrecision that is twice the PrecisionGoal. For this particular integral, the oscillations near zero cause problems eventhough the automatic method used appears to be OscillatorySelection (identical results).

(tab = Table[{n, NIntegrate[Exp[Sin[1/x]], {x, 0, \[Pi]/2},
       WorkingPrecision -> n, PrecisionGoal -> 15,
       Exclusions -> (x == 0)] // Quiet}, {n, 15, 50, 5}]) // Grid


Bob Hanlon

---- Alexei Boulbitch <alexei.boulbitch at iee.lu> wrote: 

=============

NIntegrate[Exp[Sin[1/x]], {x, 0, \[Pi]/2}, WorkingPrecision -> 12,
   Exclusions -> (x == 0), PrecisionGoal -> 15] // Quiet

3.09892833696

    * /Subject/: [mg114668] Calculate a numerical integral with enough
      precision
    * /From/: alphatest <iliurarfwpuap at mailinator.com>
    * /Date/: Sun, 12 Dec 2010 05:45:17 -0500 (EST)

------------------------------------------------------------------------

How can we calculate the following integral up to 10-12 decimal places?

integrate exp(sin(1/x)) , x=0..pi/2

It's as if no integration method or precision option lets you calculate more than 5-6 decimal places. Is it possible?



-- 
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