Re: piecewise integration
- To: mathgroup at smc.vnet.net
- Subject: [mg66961] Re: [mg66944] piecewise integration
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 5 Jun 2006 03:48:18 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
load[x_]=-9*10^3*
DiracDelta[x]+Piecewise[{{x*10*(10^3/3),0â?¤xâ?¤3}},0]-6*10^3*DiracDelta[x-5];
If a bound of the integration is on a DiracDelta then Mathematica integrates that DiracDelta to 1/2 of its coefficient
Integrate[DiracDelta[x],{x,0,1}]
1/2
Integrate[DiracDelta[x],{x,-1,0}]
1/2
Integrate[DiracDelta[x],{x,-1,1}]
1
This impacts both ends of your integral
Integrate[#,{x,0,5}]&/@load[x]
7500
Integrate[#,{x,0,6}]&/@load[x]
4500
Integrate[#,{x,-1,5}]&/@load[x]
3000
Integrate[#,{x,-1,6}]&/@load[x]
0
Bob Hanlon
---- Chris Chiasson <chris at chiasson.name> 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}]
>
> --
> http://chris.chiasson.name/
>
--
Bob Hanlon
hanlonr at cox.net