Re: A bug in Integrate ?

• To: mathgroup at smc.vnet.net
• Subject: [mg56404] Re: A bug in Integrate ?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Sun, 24 Apr 2005 03:28:54 -0400 (EDT)
• References: <d4ak8d\$io0\$1@smc.vnet.net> <d4cmhj\$38o\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Scout" <user at domain.com> wrote:
> There is no bug at all!
>
> Integrate[Exp[-x]UnitStep[-x], {x, a, Infinity}]
> and
> -Integrate[Exp[-x]UnitStep[-x], {x, Infinity, a}]
>
>  return the same result:    (-1+E^-a) UnitStep[-a]

I don't know what version you or Stepan are using, but using version
5.1.0.0 under Windows XP, Mathematica claims that the second integral
"does not converge on (Infinity, a)." But of course that interval looks
rather strange!

By using an assumption, however, we can get a correct answer:

In[6]:=
Assuming[Element[a, Reals], -Integrate[Exp[-x] UnitStep[-x], {x, Infinity, a}]]

Out[6]=
-(1-Cosh[a]+Sinh[a]) UnitStep[-a]

David Cantrell

> "Stepan Yakovenko" <yakovenko-mg at ngs.ru> ha scritto nel messaggio
> news:d4ak8d\$io0\$1 at smc.vnet.net...
> > Hello !
> >
> > Strange, but
> >
> > Integrate[Exp[-x]UnitStep[-x], {x, a, Infinity}]
> >
> > calculates integral right, but
> >
> > -Integrate[Exp[-x]UnitStep[-x], {x, Infinity, a}]
> >
> > says that it doesn't converge.

```

• Prev by Date: xhtml + mathml + NotebookWrite
• Next by Date: Re: Re: SpinShow problem
• Previous by thread: Re: Re: A bug in Integrate ?
• Next by thread: Can I make permanent font settings in Mathematica 5