Re: Re: Integral confusion
- To: mathgroup at smc.vnet.net
- Subject: [mg107316] Re: [mg107297] Re: Integral confusion
- From: "Nasser M. Abbasi" <nma at 12000.org>
- Date: Tue, 9 Feb 2010 02:44:02 -0500 (EST)
- References: <hkm7d8$os0$1@smc.vnet.net> <201002080836.DAA29853@smc.vnet.net> <op.u7tlcde4tgfoz2@bobbys-imac.local>
- Reply-to: "Nasser M. Abbasi" <nma at 12000.org>
The "weird" thing is not what specific constant of integration it returned, but the fact that it did return one at all. Integrate[x^2, x] gives x^3/2. not x^3/2+Pi*Sqrt[-1] or x^3/2+99 even though both are correct. > I don't know Integrate's steps in obtaining the result, but I'm sure it > didn't add extraneous constants deliberately. Ofcourse. I am sure of that too. But the final result is NOT what one would normally see in a textbook or expect or do when solving by hand, even though as I said, it is correct. It is just not "normal" looking. I am sorry, I did not mean to say anything bad about Mathematica when I said this result was "weird" even though it is correct. --Nasser ----- Original Message ----- From: "DrMajorBob" <btreat1 at austin.rr.com> To: "Nasser M. Abbasi" <nma at 12000.org>; <mathgroup at smc.vnet.net> Sent: Monday, February 08, 2010 9:54 AM Subject: [mg107316] Re: [mg107297] Re: Integral confusion >> But Mathematica does (normally?) return results for indefinite integrals >> without an explicit constant of integration. > > What's "explicit" or weird about the constants of integration in this > problem? > > I don't know Integrate's steps in obtaining the result, but I'm sure it > didn't add extraneous constants deliberately. > > Bobby > > On Mon, 08 Feb 2010 02:36:16 -0600, Nasser M. Abbasi <nma at 12000.org> > wrote: > >> >> "Jon Joseph" <josco.jon at gmail.com> wrote in message >> news:hkm7d8$os0$1 at smc.vnet.net... >>> All: Is this integral wrong? If not could someone explain the minus sign >>> inside the log? >>> >>> Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify >>> >>> log(-2 (x + 1)) - log(2 (x + 6)) >>> >>> Thanks, Jon.= >>> >> >> Well, lets see: >> >> log(-2 (x + 1)) - log(2 (x + 6)) >> = log(-2)+log(1+x) -log(2)-log(x+6) >> = log(-1)+log(2)+log(1+x)-log(2)-log(x+6) >> = log(-1)+ log(1+x) - log(x+6) >> >> but log(-1) = Sqrt[-1]*Pi >> >> so result is >> >> Sqrt[-1]*Pi + log(1+x) - log(x+6) >> >> But we all know that the result should be >> >> log(1+x) - log(x+6) >> >> So, an extra term, Sqrt[-1]*Pi term pops up. But this term is a >> constant, so >> its derivative is zero, i.e. a constant of integration. >> >> Since >> >> D[log(-2 (x + 1)) - log(2 (x + 6)),x] will give back >> >> 1/(x + 1) - 1/(x + 6) >> >> So, in theory, the answer given by Mathematica is NOT wrong. >> >> But Mathematica does (normally?) return results for indefinite integrals >> without an explicit constant of integration. So I am not sure why it >> does in >> this case, and if it it does, why did not pick this constant? Why not >> C[1] >> as it does for DSolve[]? >> >> So, if I have to guess, I'd say this result is at least very weired, but >> mathematically it is not wrong? >> >> --Nasser >> >> >> > > > -- > DrMajorBob at yahoo.com
- Follow-Ups:
- Re: Re: Re: Integral confusion
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: Re: Re: Integral confusion
- References:
- Re: Integral confusion
- From: "Nasser M. Abbasi" <nma@12000.org>
- Re: Integral confusion