Re: The Integrator (Wolfram)
- To: mathgroup at smc.vnet.net
- Subject: [mg26898] Re: The Integrator (Wolfram)
- From: "Paul Lutus" <nospam at nosite.com>
- Date: Fri, 26 Jan 2001 23:29:44 -0500 (EST)
- References: <94r83n$ih0@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Phil Freedenberg" <pfreedenberg at hotmail.com> wrote in message news:94r83n$ih0 at smc.vnet.net... > > Hello > Are you aware that if you integrate Sqrt[1 + a/x^(0.5)] you get zero but > the integral of Sqrt[1 + a/x^(1/2)] looks correct? Is this a bug? When Mathematica is presented with a floating-point constant, its behavior changes. Unless precautions are taken(*), it will use what are called "machine-precision numbers," numbers whose accuracy depends on the platform's own floating-point resources. This remark applies only to floating-point values, not to integers or undefined variable names or variables to which integers have been assigned. To experiment with this difference, write the equation in two ways: f1[x_] := Sqrt[1 + a/x^(0.5)] f2[x_] := Sqrt[1 + a/x^(1/2)] Note the difference when integers or unassigned variable names are applied to the two functions. f1[5] = Sqrt[1 + 0.447214 a] f2[5] = a Sqrt[1 + -------] Sqrt[5] This difference is discussed at length in the Mathematica documentation ("3.1.4 Numerical Precision"). * One precaution is to force a FP number to be larger than machine-precision range. This increases resolution arbitrarily, but it doesn't prevent some of the undesirable behavior in the above example. To force a FP number to be taken as larger than it would otherwise be interpreted, enter it this way: 0.5`100 (* means 0.5 followed by 100 zeros *) -- Paul Lutus www.arachnoid.com