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

*To*: mathgroup at smc.vnet.net*Subject*: [mg100767] Re: [mg100727] Correction to "Fundamental Theorem of Calculus and Mathematica"*From*: Curtis Osterhoudt <cfo at lanl.gov>*Date*: Sat, 13 Jun 2009 06:04:10 -0400 (EDT)*Organization*: LANL*References*: <200906120144.VAA17857@smc.vnet.net>*Reply-to*: cfo at lanl.gov

Works here ("7.0 for Linux x86 (32-bit) (November 11, 2008)"). In[4]:= f[x_] := Integrate[Sin[t^2], {t, 0, x}] In[5]:= D[f[x], x] Out[5]= Sin[x^2] In[6]:= g[x_] := Integrate[Exp[-t^2], {t, 0, x}] In[7]:= D[g[x], x] Out[7]= E^-x^2 On Thursday 11 June 2009 07:44:34 pm 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 > > -- ================================== Curtis Osterhoudt cfo at remove_this.lanl.and_this.gov PGP Key ID: 0x4DCA2A10 ==================================

**References**:**Correction to "Fundamental Theorem of Calculus and Mathematica"***From:*Len <lwapner2@gmail.com>