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Re: Correction to "Fundamental Theorem of Calculus and

• To: mathgroup at smc.vnet.net
• Subject: [mg100746] Re: [mg100727] Correction to "Fundamental Theorem of Calculus and
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 12 Jun 2009 05:46:33 -0400 (EDT)
• Reply-to: hanlonr at cox.net

Works in my version.

$Version

7.0 for Mac OS X x86 (64-bit) (February 19, 2009)

f[x_] := Integrate[Sin[t^2], {t, 0, x}]

D[f[x], x]

Sin[x^2]

g[x_] := Integrate[Exp[-t^2], {t, 0, x}]

D[g[x], x]

E^(-x^2)


Bob Hanlon

---- Len <lwapner2 at gmail.com> 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

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