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 / 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

**Follow-Ups**:**Re: Re: Integrate question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>