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MathGroup Archive 2002

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Calculus`Integration` in Math 4.1 with Win98

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35198] Calculus`Integration` in Math 4.1 with Win98
  • From: "Raf" <r_a_f at yahoo.it>
  • Date: Mon, 1 Jul 2002 03:34:56 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
Some questions about Calculus`Integration`:
1)
In[1]:= <<Calculus`Integration`
This doesn't work:
In[2]:= Integrate[FractionalPart[t], {t, 0, 5}]
Out[2]= Integrate[FractionalPart[t], {t, 0, 5}]
This works:
In[3]:= Integrate[FractionalPart[t]*Boole[t<Infinity], {t, 0, 5}]
Out[3]= 5/2

Can I avoid to write everytime Boole[t<Infinity] or similar and have the
right answer?

2)
Defining...
In[4]:= ondTri[t_] := 4Abs[t - Floor[t] - 1/2] - 1
This works:
In[5]:= Integrate[ondTri[t]*Boole[t < Infinity], {t, 0, 1/8}]
Out[5]= 3/32
This not:
In[5]:= Integrate[ondTri[t]*Boole[t < Infinity], {t, 0, 0.125}]

Mathematica answers with many error messages ( and sometimes the kernel
crash )
Why?

3)
This regards not only Calculus`Integration`, but also the built-in
Integrate:
Defining a square wave...
In[1]:= ondQua[t_] := If[OddQ[Floor[2t]], -1, 1]
....Mathematica fails completely in computing its defined integral...
In[2]:= Integrate[ondQua[t], {t, 0, 1}]
Out[2]= 1
....without any warning or error message !!!
How is it possible?

With NIntegrate the things goes better, but i believe that a similar risk
with Integrate would have to be documented somewhere; if exists some notes
about this using of Integrate on Mathematica-help, please tell me where.

Waiting your answers,
Thanks,
Raf.







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