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

```

• Prev by Date: Re: Integration Problem
• Next by Date: Re: Problem in using preassigned variable in manipulate
• Previous by thread: Re: Integration Problem
• Next by thread: New to Mathematica