Re: Tough Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg92673] Re: Tough Limit
- From: Peter Pein <petsie at dordos.net>
- Date: Fri, 10 Oct 2008 04:34:07 -0400 (EDT)
- References: <gckmsj$nh8$1@smc.vnet.net>
carlos at colorado.edu schrieb:
> How can I get
>
>
> Limit[Integrate[Sin[\[Omega]*t]*Exp[-s*t],{t,0,x},
> Assumptions->s>0],x->\[Infinity]]
>
> to answer \[Omega]/(\[Omega]^2+s^2) ?
>
Keeping in mind that
Integrate[f[x],{x,x0,Infinity}] is by def.
Limit[Integrate[f[x],{x,x0,x1},x1->Infinity],
Integrate[Sin[\[Omega]*t]*Exp[-s*t],{t,0,Infinity},Assumptions -> s>0]
or
LaplaceTransform[Sin[\[Omega]*t],t,s]
should (don't have Mathematica installed on this system) give the desired result.