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Re: Help -- Weird integration behavior

• To: mathgroup at smc.vnet.net
• Subject: [mg49353] Re: [mg49345] Help -- Weird integration behavior
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 16 Jul 2004 06:06:35 -0400 (EDT)
• References: <200407151100.HAA11167@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 15 Jul 2004, at 20:00, Mike wrote:

> *This message was transferred with a trial version of CommuniGate(tm) 
> Pro*
> I'm working on a project that I last worked on a couple of years ago,
> and I'm trying to pick up where I left off. I had been doing some
> integrations using Mathematica 4.2, and all was well. I'm now trying
> to use the same workbook, but with Mathematica 5.0, and the
> integration that previously seemed to work now gives me a value of
> zero.
>
> Interestingly, when I run the same file on different versions of
> Mathematica, I get either zero or an expression:
>
> --v5.0 (student), Macintosh: zero
> --v5.0, Solaris: zero
> --v4.2, Macintosh: expression
> --v4.0, Windows: expression
>
> Here's the code:
> F[x_, t_] = (ks (UnitStep[x] - UnitStep[x - 0.5]))(UnitStep[t] -
> UnitStep[t - 0.5]);
> phi[n_, x_] = Sqrt[2] Sin[n Pi x/L]
> G[n_, t_] = Integrate[F[x, t] phi[n, x], {x, 0, L}]
>
> It's the output of this last line that's interesting to me -- either
> an expression (I hope) or zero. My questions are:
>
> -- Did something change in 5.0 that makes it so that this integration
> doesn't work correctly?
> -- Can anybody out there reproduce my problem (i.e., run these three
> cells on different versions and produce different answers?)
>
> Thanks for the help!
>
>
Yes, things have changed ;-(

However:


F[x_, t_] = (ks*(UnitStep[x] - UnitStep[x - 0.5]))*
     (UnitStep[t] - UnitStep[t - 0.5]);
phi[n_, x_] = Sqrt[2]*Sin[n*Pi*(x/L)];


Simplify[Integrate[F[x, t]*phi[n, x], {x, 0, L},
    GenerateConditions -> False]]


(1/(n*Pi))*(Sqrt[2]*ks*L*
    ((Cos[(1.5707963267948966*n)/L] - Cos[n*Pi])*
      UnitStep[L - 0.5] + (Cos[n*Pi] - 1)*UnitStep[L])*
    (UnitStep[t - 0.5] - UnitStep[t]))

This is actually a better answer than Mathematica 4.2 gives, since in 
Mathematica 4.2 you will only get a satisfactory answer if you use 1/2 
instead 0.5.


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

• References:
  • Help -- Weird integration behavior
    • From: miked378@hotmail.com (Mike)