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

• To: mathgroup at smc.vnet.net
• Subject: [mg100773] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Sat, 13 Jun 2009 06:05:15 -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

Hi, Len,
I tried and this is the result:

In[3]:= g[x_] := Integrate[Exp[-t^2], {t, 0, x}]

In[4]:= D[g[x], x]

Out[4]= \[ExponentialE]^-x^2

Sorry, Alexei

--
Alexei Boulbitch, Dr., habil.
Senior Scientist

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