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 -- +---------------------------------+ | Gianluca Gorni | | Universita` di Udine | | Dipartimento di Matematica | | e Informatica | | via delle Scienze 208 | | I-33100 Udine UD | | Italy | +---------------------------------+ | Ph.: (39) 0432-558422 | | Fax: (39) 0432-558499 | | mailto:gorni at dimi.uniud.it | | http://www.dimi.uniud.it/~gorni | +---------------------------------+