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

*To*: mathgroup at smc.vnet.net*Subject*: [mg100750] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 13 Jun 2009 06:01:03 -0400 (EDT)*Organization*: Uni Leipzig*References*: <h0sbtl$hdk$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, this is nonsens. f[x_] := Integrate[Sin[t^2], {t, 0, x}] g[x_] := Integrate[Exp[-t^2], {t, 0, x}] D[#, x] & /@ {g[x], f[x]} gives {E^(-x^2), Sin[x^2]} That is why it is useful to post your full input and not a verbal description. Regards Jens 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 >