Re: Simple question or how Mathematica getting on my nerves.

*To*: mathgroup at smc.vnet.net*Subject*: [mg45783] Re: [mg45779] Simple question or how Mathematica getting on my nerves.*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 25 Jan 2004 03:04:39 -0500 (EST)*References*: <200401240536.AAA07517@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 24 Jan 2004, at 05:36, George wrote: > Although the 2 results must be the same they aren't. WHY??????? > And not only this, but they differ by 10^21!!!!!! WHY???????? > > Please copy and paste this to Mathematica (i tried 5.0 and 4.2) to > understand what i mean: > > > \!\(k[f_] := > 2687176093959399272413585923303421161600\ *\((1 - f)\)\^67\ * > f\^61\[IndentingNewLine] > N[\[Integral]\_\(6214\/10000\)\%\(5242\/10000\)k[ > f] \[DifferentialD]f]\[IndentingNewLine] > N[\[Integral]\_0.6214\%0.5242 k[f] \[DifferentialD]f]\) > > No, they mustn't be the same, at least not in Mathematica. In Mathemtica, 6214/10000 and 0.6214 are not at all the same, since Precision[0.6214] MachinePrecision Precision[6214/10000] Infinity You need a lot of precision in the limits in your case to get an accurate answer, compare: k[f_] := 2687176093959399272413585923303421161600* (1 - f)^67*f^61 Integrate[k[f], {f, N[6214/10000, MachinePrecision], N[5242/10000, MachinePrecision]}] 2.056906588664101*^22 Integrate[k[f], {f, N[6214/10000, 20], N[5242/10000, 20]}] 0``-20.81782624184503 Integrate[k[f], {f, N[6214/10000, 50], N[5242/10000, 50]}] -0.1398383104167567265`8.464671124714428 Only the last answer is accurate. Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Simple question or how Mathematica getting on my nerves.***From:*gtsavdar@auth.gr (George)