Re: Correction to "Fundamental Theorem of Calculus and Mathematica"

*To*: mathgroup at smc.vnet.net*Subject*: [mg100766] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Sat, 13 Jun 2009 06:03:59 -0400 (EDT)*References*: <h0sbtl$hdk$1@smc.vnet.net>

Len wrote: > Greetings: > > I define a function (using f[x_]:=) as the definite integral (from 0 > to x) of sin(t^2). When I differentiate using Mathematica I get the > correct answer of sin(x^2). > > But when I define a function (using g[x_]:=) as the definite integral > (from 0 to x) of e^(-t^2) and differentiate, I get the incorrect > answer of 0. (The correct answer is e^(-x^2).) > > Why the inconsistency? > > Oddly, if I define the function g above using "=" instead of ":=", all > works well. > > Can someone explain the odd behavior? > > Thanks, > > Len > My guess is that you had been doing things with Mathematica prior to that, and as a result, g had some sort of definition. If the problem happens again, try typing ??g If you get a strange result, it is often useful to kill the kernel so that you start with a clean slate. David Bailey http://www.dbaileyconsultancy.co.uk