Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: piecewise integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66963] Re: piecewise integration
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 5 Jun 2006 03:48:27 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e5tt8l$ebs$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Chiasson wrote:
> The Integrate result seems pretty weak. Is there any way to obtain a
> more explicit exact answer besides manually converting the Piecewise
> function to two UnitStep functions? Can the same be done if the final
> limit of integration is a variable?
> 
> in
> 
> load[x_]=-9*10^3*DiracDelta[x]+Piecewise[{{x*10*(10^3/3),0<=x<=3}}]-6*10^3*DiracDelta[x-5]//InputForm
> 
> out
> 
> -6000*DiracDelta[-5 + x] - 9000*DiracDelta[x] +
> Piecewise[{{(10000*x)/3, 0 <= x <= 3}}, 0]
> 
> in
> 
> Integrate[load[x],{x,0,5}]//InputForm
> 
> out
> 
> Integrate[InputForm[-6000*DiracDelta[-5 + x] - 9000*DiracDelta[x] +
> Piecewise[{{(10000*x)/3, 0 <= x <= 3}}, 0]], {x, 0, 5}]
> 
Hi Chris,

You could try Maxim Rytin's PiecewiseIntegrate function [1].

 From MathSource: "The notebook contains the implementation of four 
functions PiecewiseIntegrate, PiecewiseSum, NPiecewiseIntegrate, 
NPiecewiseSum. They are intended for working with piecewise continuous 
functions, and also generalized functions in the case of 
PiecewiseIntegrate. They support all the standard Mathematica piecewise 
functions such as UnitStep, Abs, Max, as well as Floor and other 
arithmetic piecewise functions. PiecewiseIntegrate supports the 
multidimensional DiracDelta function and its derivatives. The arguments 
of the piecewise functions can be non-algebraic and contain symbolic 
parameters."

In[1]:=
load[x_] := -6000*DiracDelta[-5 + x] -
    9000*DiracDelta[x] + Piecewise[
     {{(10000*x)/3, 0 <= x <= 3}}, 0]

In[2]:=
Integrate[load[x], {x, 0, 5}]

Out[2]=
Integrate[-6000*DiracDelta[-5 + x] -
    9000*DiracDelta[x] + Piecewise[
     {{(10000*x)/3, 0 <= x <= 3}}], {x, 0, 5}]

In[103]:=
PiecewiseIntegrate[load[x], {x, 0, 5}]

Out[103]=
0

HTH,
Jean-Marc

[1]: Rytin, Maxim, _Integration of Piecewise Functions with 
Applications_, Mathematica Package, 
http://library.wolfram.com/infocenter/MathSource/5117/


  • Prev by Date: Re: Re: New Analytical Functions - Mathematica Verified
  • Next by Date: Re: piecewise integration
  • Previous by thread: Re: piecewise integration
  • Next by thread: Re: piecewise integration