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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
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