integral of x^n
- To: mathgroup at smc.vnet.net
- Subject: [mg130575] integral of x^n
- From: Richard Fateman <fateman at cs.berkeley.edu>
- Date: Tue, 23 Apr 2013 00:03:24 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
- References: <20130420094229.B63996A64@smc.vnet.net> <20130421091626.26FB96AC3@smc.vnet.net> <kl2nvm$2di$1@smc.vnet.net>
On 4/22/2013 12:13 AM, Alex Krasnov wrote: > In this case, the results are valid for a=1 in the sense of a limit, as > Limit[u, a -> 1] and limit(u, a, 1) demonstrate. This is not always the > case. Example: > > In: f = Integrate[x^n, x] > Out: x^(1 + n)/(1 + n) > > In: Limit[f, n -> -1, Direction -> 1] > Out: -Infinity > > In: Limit[f, n -> -1, Direction -> -1] > Out: Infinity > > Alex > > Yes, but an equally valid antiderivative for x^n is s = (x^(n+1)-1)/(n+1). note Limit[s,n->-1] is Log[x]. This alternative formula was, I think, pointed out more than once to Wolfram Inc. probably circa version 2. There are other issues that come up when using antiderivatives + the fundamental theorem of integral calculus. Some of these become apparent by reading FTIC carefully. RJF
- References:
- Mathematica integration Vs Sympy
- From: Sergio R <sergiorquestion@gmail.com>
- Re: Mathematica integration Vs Sympy
- From: Brentt <brenttnewman@gmail.com>
- Mathematica integration Vs Sympy