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Re: Add the Logarithms (error in integral)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25157] Re: Add the Logarithms (error in integral)
*From*: Jos R Bergervoet <Jos.Bergervoet at philips.com>
*Date*: Tue, 12 Sep 2000 02:58:45 -0400 (EDT)
*Organization*: Philips Research Laboratories
*References*: <8p9j71$1fl@smc.vnet.net> <KGVu5.30316$Zh6.36755@ralph.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Jens-Peer Kuska wrote:
>
> h1 = h //. a_.*Log[b_] + c_.*Log[d_] :> Log[b^a*d^c];
>
> Chop[N[h1 /. {a -> 10, b -> 10}]]
>
> 0.000716695
The trick seems interesting. But the answer is incorrect (for
a=b=10 it must be ArcTan[50/Sqrt[101]], which is:
1.3724418046360918933042446254231305679...
-- Jos
> > 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.
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