Re: Integration Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg126366] Re: Integration Problem*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Thu, 3 May 2012 22:25:33 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205030834.EAA29972@smc.vnet.net>

Integrate[E^(-1/10 ((1 + r2z)^2)), {r2z, -Infinity, Infinity}] Sqrt[10 \[Pi]] % // N 5.60499 Integrate[E^(-0.1 ((1 + r2z)^2)), {r2z, -Infinity, Infinity}] 5.60499 - 2.03152*10^-16 I The use of an inexact number (0.1) results in the calculation being done with machine precision that keeps the complex part from cancelling exactly. This artifact can be removed with Chop. % // Chop 5.60499 Alternatively, you can use NIntegrate which doesn't involve any intermediate complex representations. NIntegrate[E^(-0.1 ((1 + r2z)^2)), {r2z, -Infinity, Infinity}] 5.60499 Bob Hanlon On Thu, May 3, 2012 at 4:34 AM, Michael Musheghian <michael.musheghian at gmail.com> wrote: > Greetings! > > I found that evaluation of this 2 integrals yield a bit different result. What could be the reason? > > Integrate[E^(-1/10 ((1 + r2z)^2)), {r2z, -Infinity, Infinity}] > > Integrate[E^(-0.1 ((1 + r2z)^2)), {r2z, -Infinity, Infinity}] >

**References**:**Integration Problem***From:*Michael Musheghian <michael.musheghian@gmail.com>