Re: Integration Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg126368] Re: Integration Problem*From*: Oliver Jennrich <oliver.jennrich at gmx.net>*Date*: Fri, 4 May 2012 06:25:35 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jntg1g$g$1@smc.vnet.net>

Michael Musheghian <michael.musheghian at gmail.com> writes: > 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}] Numerics. The first integral evaluates symbolically, the second one semi-numerically. Mathematica 8 yields Sqrt[10 \[Pi]] for the former and 5.60499 - 2.03152*10^-16 I for the latter. You can avoid the very small imaginary part by either calculating the equivalent integral Integrate[E^(-0.1 ((r2z)^2)), {r2z, -Infinity, Infinity}] (i.e. performing a shift in the integration variable) or by having Mathematica calculate the integral fully symbolically: Integrate[E^(-a ((r2z)^2)), {r2z, -Infinity, Infinity}, Assumptions -> {a > 0}] which yields not surprisingly Sqrt[\[Pi]]/Sqrt[a] -- Space - The final frontier