Re: need help with integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg52024] Re: [mg51997] need help with integration*From*: DrBob <drbob at bigfoot.com>*Date*: Sun, 7 Nov 2004 01:04:18 -0500 (EST)*References*: <200411060708.CAA26072@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

I assume you mean eq2 + eq3 - eq1 // FullSimplify (3*(-2 + t))/Sqrt[(-2 + t)^2] - (3*t)/Sqrt[t^2] - 6*UnitStep[-2 + t] + (6*(E*UnitStep[-2 + t] - UnitStep[t]))/E^(t/2) + 6*UnitStep[t] should be zero for all t? If we reduce x[t] to just x[t_]=3Exp[-.5t]UnitStep[t] or x[t_]=DiracDelta[t + 3], it works properly, so I think it should work for your x function as well. But it doesn't. Perhaps, when we add the terms together, there's some ambiguity about the value at -3, and that leads to the problem? Hopefully the experts can tell you more. Bobby On Sat, 6 Nov 2004 02:08:53 -0500 (EST), symbio <symbio at has.com> wrote: > > > Below I define two functions x[t] and h[t], then in eq1 I integrate > the integrand ( x[tau] h[t-tau] ) from -inf to +inf and get one set of > results and plots, then I integrate the same integrand as before but this > time in two steps, once from -inf to 0 and once from 0 to +inf, but the > results and plots from the integration performed in two steps are NOT the > same as the results and plots from integration in one step. Is this a bug > and if so what's the work around? > > Try this in the input cell > > In[19]:= > x[t_] = (3Exp[-.5t]UnitStep[t]) + DiracDelta[t + 3] > h[t_] = UnitStep[t] - UnitStep[t - 2] > eq1 = Integrate[x[\[Tau]]h[t - \[Tau]], {\[Tau], -\[Infinity], \[Infinity]}] > Plot[eq1, {t, -10, 10}, PlotRange -> All] > eq2 = Integrate[x[\[Tau]]h[t - \[Tau]], {\[Tau], 0, \[Infinity]}] > Plot[eq2, {t, -10, 10}, PlotRange -> All] > eq3 = Integrate[x[\[Tau]]h[t - \[Tau]], {\[Tau], -\[Infinity], 0}] > Plot[eq3, {t, -10, 0}, PlotRange -> All] > > You will get the following output expressions (I couldn't paste the plots > here, but if you run the above input cells you should get the plots too, > then it will be more obvious what the problem is) > > Out[21]= > \!\(1\/2\ \((1 + \(6.`\ \@\((\(-2\) + t)\)\^2\)\/\(\(\(2.`\)\(\ > \[InvisibleSpace]\)\) - 1.`\ t\) + \(6.`\ \@t\^2\)\/t + \@\((3 + > t)\)\^2\/\(3 \ > + t\) - \(1 + t + \@\((1 + t)\)\^2\)\/\(1 + t\))\)\) > > > > Out[23]= > \!\(\((\(-6.`\) + > 16.30969097075427`\ \[ExponentialE]\^\(\(-0.5`\)\ t\))\)\ UnitStep[\ > \(-2\) + t] + \((\(\(6.`\)\(\[InvisibleSpace]\)\) - > 6.`\ \[ExponentialE]\^\(\(-0.5`\)\ t\))\)\ UnitStep[t]\) > > > > Out[25]= > \!\(1\/2\ \((\(-\(\(1 + > t\)\/\@\((1 + t)\)\^2\)\) + \(3 + t\)\/\@\((3 + t)\)\^2)\)\) > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**need help with integration***From:*"symbio" <symbio@has.com>