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MathGroup Archive 2000

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Re: strange Integrate result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24440] Re: [mg24394] strange Integrate result
  • From: "Richard Finley" <rfinley at medicine.umsmed.edu>
  • Date: Tue, 18 Jul 2000 00:58:40 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Gianluca,

See the help index about Mathematica's assumptions about parameters when doing definite integrals vs indefinite integrals.  For your case, try the following:

Integrate[t(1 - Cos[a* t]), {t, 0, Pi}, Assumptions -> a != 0]

and I think you will get the result you are looking for.  regards...RF

>>> Gianluca Gorni <gorni at dimi.uniud.it> 07/12/00 09:13PM >>>

Hello!

With Mathematica 4.0:

Integrate[t (1 - Cos[a*t]), {t, 0, Pi}]   gives  Indeterminate,

although the function is analytic everywhere.

If I define

prim[t_] = Integrate[t (1 - Cos[a*t]), t]

then prim[0] is Indeterminate too. To get the correct result I have
to Simplify[prim[t]] before setting t->0:

Subtract @@ (Simplify[prim[t]] /. {{t->Pi}, {t->0}})

There is also a related wrong Limit[] result. Define

myFunc[t_, a_] = Integrate[t^a(1 - Cos[t/3]), t] // FullSimplify;

Then

Limit[myFunc[t, a], t -> 0]  gives  0, which is wrong, because

Limit[myFunc[t, 1], t -> 0]  gives -9, that agrees with numerical trials.

Best regards,

              Gianluca Gorni

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