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Re: Stieltjes Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22538] Re: [mg22475] Stieltjes Integral
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Thu, 9 Mar 2000 03:24:24 -0500 (EST)
  • References: <200003080722.CAA13181@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Greg wrote:
> 
> Well, I just wanted to calculate Integrate[x,{x^2,0,1}] and ....... - Well
> Integrate[...] does only support Riemann integral. So, is there a package
> for free available that teaches M4 a little bit something about Stieltjes
> integral? It should be fairly trivial. But the master index of M4 does not
> list anything under the term "Stieltjes".
> 
> BTW, I know the result of the above integral and I am not looking for a
> special M4 routine that can handle only the trivial example mentioned in
> this message. The correct result is 2/3.
> 
> Thanks,
> 
> Greg

Could do:

In[1]:= stieltjesIntegrate[func1_, var_, {func2_,a_,b_}] :=
        Integrate[func1*D[func2,var], {var,a,b}]        

In[2]:= stieltjesIntegrate[x, x, {x^2,0,1}] 

        2
Out[2]= -
        3

If you want to handle singular measures you'll need something more
subtle than this.


Daniel Lichtblau
Wolfram Research


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