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Re: Add the Logarithms (error in integral)


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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