Re: Integrate function defined by numerical integration

• To: mathgroup at smc.vnet.net
• Subject: [mg124181] Re: Integrate function defined by numerical integration
• From: Hani <hanisantosa at gmail.com>
• Date: Wed, 11 Jan 2012 17:23:43 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201112170741.CAA18787@smc.vnet.net> <jckc4s\$1ig\$1@smc.vnet.net>

```On Dec 18 2011, 10:35 am, Bob Hanlon <hanlonr... at gmail.com> wrote:
> Since func is defined using numerical techniques, restrict its
> definition to numerixal arguments.
>
> Clear[func]
>
> func[x_?NumericQ] :=
>   NIntegrate[
>    x*Sec[alpha]^2*Exp[-x/Cos[alpha]],
>    {alpha, -ArcCos[x/2], ArcCos[x/2]}];
>
> NIntegrate[func[x], {x, 0.2, 1}]
>
> 1.02655
>
> Bob Hanlon
>
>
>
>
>
>
>
> On Sat, Dec 17, 2011 at 2:41 AM, Hani <hanisant... at gmail.com> wrote:
> > Hello all, I have a problem. Suppose I have a function:
>
> > func[x_] := NIntegrate[ x*Sec[alpha]^2*Exp[-x/Cos[alpha]], {alpha, -
> > ArcCos[x/2], ArcCos[x/2]}].
>
> > Basically the argument of the function, x, also appears as boundary of
> > integration
>
> > Now, when I want to do this integral:
>
> > NIntegrate[func[x], {x, 0.2, 1}]
>
> > there are error messages: NIntegrate::nlim: alpha = cos^-1(0.5 x) is
> > not a valid limit of integration. >>
>
> > Although in the end, the result appears. Now, how to handle this
> > problem? I think in this case, we can get the result because func[x_]
> > itself is simple. But actually my func[x_] is much more complicated,
> > it contains interpolating function too, and when I do the integral, it
> > takes long time without result. Can anyone help me?

Thank you Bob

```

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