Re: Integratecrashes kernel
- To: mathgroup at smc.vnet.net
- Subject: [mg50768] Re: Integratecrashes kernel
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sun, 19 Sep 2004 21:39:24 -0400 (EDT)
- References: <cije7o$hjs$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Bill Rowe <readnewsciv at earthlink.net> wrote: > On 9/18/04 at 5:48 AM, math5bug at lmm.jussieu.fr (B. Oudoli) wrote: > > >However, Integrate[x Cos[1. x], x] > >crashes the kernel, and it's impossible to abort or interrupt the > >calculation, which lasts forever. > In this specific case > > Integrate[x Cos[a x],x] > > seems to work fine. So, you could do > > Integrate[x Cos[a x],x]/.a->1 Yes, it works fine in all but the a=0 case. Since 1. is clearly not close to 0, I doubt that the comment below is related to the bug mentioned above, but I hope it might be of some interest nonetheless. The antiderivative given is Cos[a x]/a^2 + x Sin[a x]/a. Not only does this misbehave _at_ a=0, it also misbehaves as a _approaches_ 0. But in fact an antiderivative can be given which is correct for all nonzero a and which also behaves as we would like in the limit as a->0: (Cos[a x] - 1)/a^2 + x Sin[a x]/a Of course, the difference between this antiderivative and the one given by Mathematica is only a constant (with respect to x). But as a->0, its limit is x^2/2, as it should be. David Cantrell