Correction to "Fundamental Theorem of Calculus and Mathematica"

*To*: mathgroup at smc.vnet.net*Subject*: [mg100727] Correction to "Fundamental Theorem of Calculus and Mathematica"*From*: Len <lwapner2 at gmail.com>*Date*: Thu, 11 Jun 2009 21:44:34 -0400 (EDT)

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: Correction to "Fundamental Theorem of Calculus and***From:*peter <plindsay.0@gmail.com>

**Re: Correction to "Fundamental Theorem of Calculus and Mathematica"***From:*Curtis Osterhoudt <cfo@lanl.gov>