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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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