Re: NIntegrate - bug??

• To: mathgroup at smc.vnet.net
• Subject: [mg85411] Re: NIntegrate - bug??
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Sat, 9 Feb 2008 04:20:32 -0500 (EST)
• References: <foeklg\$i9b\$1@smc.vnet.net> <fogi7f\$26i\$1@smc.vnet.net>

```dh wrote:
> 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.
>

Hi Daniel,

It is not a bug.  Even though NIntegrate is HoldAll, it evaluates its
arguments before substituting in numerical values.  It does this to
achieve better performance, and to be able to compile the expression
when possible.

Making NIntegrate not evaluate its arguments would probably lead to an
even greater confusion:  think about cases like

a = x^2
NIntegrate[a, {x, 0, 1}]

(or using % instead of 'a')

When the function in question is evaluated with the *symbolic* arguments
expN[x, 1/5], the result is 1 + 0.2 x, and
NIntegrate[1 + 0.2 x, {x, 10, 20}] is 40.

It is easy to see why the function evaluates to 1 + 0.2 x if we keep in
mind that While[] stops as soon as the condition evaluates to something
else than True (not necessarily False).

When in doubt, use Trace[], or On[] and Off[]:

On[]
expN[x, 1/5]
Off[]

Szabolcs

```

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