       Re: NIntegrate - bug??

• To: mathgroup at smc.vnet.net
• Subject: [mg85373] Re: NIntegrate - bug??
• From: dh <dh at metrohm.ch>
• Date: Thu, 7 Feb 2008 22:27:49 -0500 (EST)
• References: <foeklg\$i9b\$1@smc.vnet.net>

```
Ho Costa,

put a Print statement into your function that prints "x" and you will

see that the function is called with x not evaluated. Why this happens,

I can not explain. But you can prevent this by requesting that x must be

numeric:

expN[x_?NumericQ,p1_]

Nevertheless, Wolfram needs to explain why the nonsense result of 40 is

returned, I think its simply a bug.

hope this helps, Daniel

Costa Bravo wrote:

> I have defined the function of Exp with series

>

> expN[x_, p1_] := Module[{min = 10^-20,s, u, j},

>    s = 1; u = 1; j = 1;

>    While[u *= N[p1*x/j, 20];

>          s += u; j++;

>          u > min*s];

>      s]

>

>

> The differences between Exp & expN

>

> tp = 10; tk = 20;

> Table[{x, Exp[x/5] - expN[x, 1/5]}, {x, tp, tk, 1}]

>

> (* OK 0*10^-18 *)

>

> (* I have integration Exp[x/5] with 'NIntegrate' *)

>

> NIntegrate[Exp[x/5], {x, tp, tk}]

>

> 236.045   (* OK *)

>

> (*  and  expN[x,1/5]  *)

>

> NIntegrate[expN[x, 1/5], {x, tp, tk}]

>

> 40.    (* Bad !! *)

>

> (* primitive integration expN   *)

>

> t1 = Table[expN[x, 1/5], {x, tp, tk, 1/10}];

> (Total[t1] - (t1[] + t1[[-1]])/2)/10

>

> 236.0533...   (* ~OK *)

>

> Why the integration of expN with NIntegrate is bad ?

>

> Tested with Mathematica 5.0 ,5.2 and 6

>

> PS

> If defined function expN1 ( without While !!)

>

> expN1[x_, p1_] := Module[{min = 10^-20, s, u, j},

>    s = 1; u = 1;

>    Do[u *= N[p1 x/j, 20]; s += u, {j, 30}];

>    s]

>

> NIntegrate[expN1[x, 1/5], {x, tp, tk}]

>

> 236.045 ( OK !!!! )

>

>

>

>

> Costa

>

```

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