       Re: Integrate question

• To: mathgroup at smc.vnet.net
• Subject: [mg77685] Re: Integrate question
• From: dimitris <dimmechan at yahoo.com>
• Date: Fri, 15 Jun 2007 04:25:02 -0400 (EDT)
• References: <f4omvd\$7qh\$1@smc.vnet.net><f4r10i\$639\$1@smc.vnet.net>

```I agree with this!
I should have posted my question differently.

In:=
Integrate[D[f[x], x], {x, a, b}]

Out=
-f[a] + f[b]

> int(D(y)(x),x=a..b);

b
/
|
|   D(y)(x) dx
|
/
a

> int(D(y)(x),x=a..b,'continuous');

-y(a) + y(b)

Integrate[f'[x],{x,a,b}] is NOT always f[b]-f[a].

In:= g[x_] = Integrate[ArcTan[Tan[x/2]], x];

In:= Integrate[Derivative[g][x], {x, 0, 3*(Pi/2)}]
Out= Pi^2/16

In:= FullSimplify[(D[g[x], x] /. x -> 3*(Pi/12)) - (D[g[x], x] /.
x -> 0)]
Out= Pi/8

Dimitris

/  Jens-Peer Kuska       :
> Hi dimitris,
>
> this is a very valuable question:
>
> > I am neither software enginner, nor pure mathematician but this
> > fundmental difference impressed me a lot! I am familiar
> > with the issue of generic complex values in mathematica
> > but here Mathematica "assumes" that typing Integrate[f'[x],{x,a,b}]
> > f[x] is continuous in [a,b]?
>
>
> and what happens with f'[x] if f[x] is *not* continuous in [a,b] ??
> it does not exist on every point in[a,b]?
> You can't write f'[x] if it does not exist
> and writing it mean that f'[x] exist and that the integral will be
> continuous.
>
> Regards
>    Jens

```

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