[Date Index]
[Thread Index]
[Author Index]
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[2]:=
Integrate[D[f[x], x], {x, a, b}]
Out[2]=
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[30]:= g[x_] = Integrate[ArcTan[Tan[x/2]], x];
In[34]:= Integrate[Derivative[1][g][x], {x, 0, 3*(Pi/2)}]
Out[34]= Pi^2/16
In[37]:= FullSimplify[(D[g[x], x] /. x > 3*(Pi/12))  (D[g[x], x] /.
x > 0)]
Out[37]= Pi/8
Dimitris
/ JensPeer 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
Prev by Date:
Re: Re: Problems updating Graphics3D Polygons
Next by Date:
Re: Notebook History  what is it good for?
Previous by thread:
Re: Integrate question
Next by thread:
Re: Re: Integrate question
 