Re: Integrate UnitStep, Bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg50341] Re: Integrate UnitStep, Bug?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Sat, 28 Aug 2004 04:37:53 -0400 (EDT)
• References: <200408261050.GAA16330@smc.vnet.net> <cgmmiu\$sj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```DrBob <drbob at bigfoot.com> wrote:
> I think both results are wrong, and the correct answer is Abs[b-a].

I have no idea why you think that's the correct answer, especially since
the plots which you mention below are correct (at least on my machine) and
clearly show that Abs[b-a] is incorrect.

> Unless these Plots are wrong?
>
> fr[e_] := UnitStep[-e];
> fl[e_] := UnitStep[-(e - b)];
>
> b = 2; a = 3;
> Plot[fl[e](fr[e - a] - fr[e]), {e, -5, 5}, PlotStyle ->
> {Thickness[0.01]}]
>
> b = 5; a = 3;
> Plot[fl[e](fr[e - a] - fr[e]), {e, -5, 5}, PlotStyle ->
> {Thickness[0.01]}]
>
> Bobby
>
> On Thu, 26 Aug 2004 06:50:47 -0400 (EDT), <jens at fika.de> wrote:
>
> > The following code returns the incorrect result (-a+b) UnitStep[a-b].
> > It should be Min[a,b].
> >
> > fr[e_]=UnitStep[-e];
> > fl[e_]=UnitStep[-(e-b)];
> > Integrate[fl[e](fr[e-a]-fr[e]),{e,-Infinity,Infinity},
> > Assumptions->{b>0,a>0}]
> >
> > Is this a known bug? Should I avoid using step functions with
> > Integrate?

This is clearly a bug. Whether it's previously known or not, I have no
idea. It needs to be fixed! It would be hard to "avoid using step functions
with Integrate" in many cases.

David Cantrell

```

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