Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
- To: mathgroup at smc.vnet.net
- Subject: [mg100750] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 13 Jun 2009 06:01:03 -0400 (EDT)
- Organization: Uni Leipzig
- References: <h0sbtl$hdk$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi,
this is nonsens.
f[x_] := Integrate[Sin[t^2], {t, 0, x}]
g[x_] := Integrate[Exp[-t^2], {t, 0, x}]
D[#, x] & /@ {g[x], f[x]}
gives
{E^(-x^2), Sin[x^2]}
That is why it is useful to post your full input and not a
verbal description.
Regards
Jens
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
>