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MathGroup Archive 2000

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Add the Logarithms (error in integral)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25060] Add the Logarithms (error in integral)
  • From: Jos R Bergervoet <Jos.Bergervoet at philips.com>
  • Date: Thu, 7 Sep 2000 22:28:03 -0400 (EDT)
  • Organization: Philips Research Laboratories
  • Sender: owner-wri-mathgroup at wolfram.com

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

--
  Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
  Philips Research Laboratories,             Eindhoven, The Netherlands
  Building WS01                                     FAX: +31-40-2742224
  E-mail: bergervo at natlab.research.philips.com    Phone: +31-40-2742403

--------------------------------------------------------------------
In[5]:= FullSimplify[h]

                                     2           2    4
         I         2    4       -4 (a  - I Sqrt[a  + a ] b)
Out[5]= (- ((Sqrt[a  + a ] (Log[---------------------------] - 
         2                                      2
                                        (-I + a)  b

                2           2    4
           -4 (a  + I Sqrt[a  + a ] b)                2
       Log[---------------------------])) / Sqrt[1 + a ] + 
                          2
                   (I + a)  b

         2       2
  (Sqrt[a  (1 + b )] (-Log[

                              2       2                        2
          -4 (-I + a) b Sqrt[a  (1 + b )] - 4 a (a + (-I + a) b )
          -------------------------------------------------------] + 
                                        2
                                (-I + a)  b

                              2       2                       2
           -4 (I + a) b Sqrt[a  (1 + b )] - 4 a (a + (I + a) b )
       Log[-----------------------------------------------------])) / 
                                       2
                                (I + a)  b

             2
   Sqrt[1 + b ])) / a


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