Re: Correction to "Fundamental Theorem of Calculus and

*To*: mathgroup at smc.vnet.net*Subject*: [mg100746] Re: [mg100727] Correction to "Fundamental Theorem of Calculus and*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 12 Jun 2009 05:46:33 -0400 (EDT)*Reply-to*: hanlonr at cox.net

Works in my version. $Version 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) f[x_] := Integrate[Sin[t^2], {t, 0, x}] D[f[x], x] Sin[x^2] g[x_] := Integrate[Exp[-t^2], {t, 0, x}] D[g[x], x] E^(-x^2) Bob Hanlon ---- Len <lwapner2 at gmail.com> 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

**Follow-Ups**:**Re: Re: Correction to "Fundamental Theorem of***From:*Mauricio Esteban Cuak <cuak2000@gmail.com>