Re: Integrate vs NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg89149] Re: Integrate vs NIntegrate
• From: "Armen Kocharyan" <armen.kocharyan at gmail.com>
• Date: Tue, 27 May 2008 07:14:27 -0400 (EDT)
• References: <2b8d8f40805252204g6aca77a0tf53fc8c31779c64a@mail.gmail.com>

```My guess is that it's a bug. Mathematica adds two different constants to
two branches (x<2, x>2). The following "fixes" the problem

Clear[x];
q = -1/2;
h[x_] = (1 + x^3)^q;

(*wrong f-fw*)
fw[x_] = Integrate[h[x], x];
fw1[x_] = (fw[x] - fw[0])*UnitStep[2 - x];
fw2[x_] = (fw[x] + fw[2] - Im[fw[3]] \[ImaginaryI])*UnitStep[x - 2];

(*right f-fr*)
fr[x_] = fw1[x] + fw2[x];

(*correct f*)
f[x_] = Integrate[h[z], {z, 0, x}, Assumptions -> x >= 0];

(*correct and wrong  f*)
Plot[{f[x], Re[fw[x]], Im[fw[x]]}, {x, 0, 10}]

(*fixed f*)
Plot[fr[x], {x, 0, 10}]

One may have to fix fr[2] as well.

Regards,
Armen

2008/5/26 Armen Kocharyan <armen.kocharyan at gmail.com>:

> Dear group,
>
>
> Why do I get different results (Res1, Res2) in Mathematica 6.0.1.0?
>
>
> *q=-1/2; a=0; b=3;*
>
> *h[x_]=(1+x^3)^q;*
>
> *f[x_]=Integrate[h[x],x];*
>
> *Res1=N[f[b]-f[a]]*
>
> *Res2=NIntegrate[h[x],{x,a,b}]*
>
> **
>
> *Res1 = -2.55387-2.42865 i*
>
> *Res2 = 1.65267*
>
>
>
> I'm assuming that Res2 is the correct answer.
>
>
>
> Regards,
>
> Armen
>

```

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