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

• To: mathgroup at smc.vnet.net
• Subject: [mg100766] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sat, 13 Jun 2009 06:03:59 -0400 (EDT)
• References: <h0sbtl$hdk$1@smc.vnet.net>

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
> 
My guess is that you had been doing things with Mathematica prior to 
that, and as a result, g had some sort of definition. If the problem 
happens again, try typing

??g

If you get a strange result, it is often useful to kill the kernel so 
that you start with a clean slate.

David Bailey
http://www.dbaileyconsultancy.co.uk