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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>