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MathGroup Archive 2000

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Re: Add the Logarithms (error in integral)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25106] Re: Add the Logarithms (error in integral)
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sun, 10 Sep 2000 03:14:29 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <8p9j71$1fl@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

h1 = h //. a_.*Log[b_] + c_.*Log[d_] :> Log[b^a*d^c];

Chop[N[h1 /. {a -> 10, b -> 10}]]

0.000716695

Regards
  Jens

Jos R Bergervoet wrote:
> 
> I'm trying to integrate a function f over a triangle with vertices:
> (0,0), (a,0), (0,b). My input is:
> 
>   f = 1/ Sqrt[1+x^2+y^2]^3
>   g = Integrate[f, {y,0, b-b x/a} ]
>   h = Integrate[g, {x,0,a}]
>   N[ h /. {a->10, b->10} ]
> 
> With a=b=10, the output for this positive(!) function is negative:
> 
>   Out[4]= -4.91074 + 0. I
> 
> which is obviously wrong.
> 
> Looking at the answer with FullSimplify[h] I see it contains 4
> logarithms (see answer at the end of this message). Is there any
> way to add these logarithms? (into one logarithm with the product
> of the original arguments?)
> 
> FullSimplify refuses to do this. Is there another way?
> 
> Thanks in advance,
> Jos


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