       Re: FindRoot and NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg81881] Re: FindRoot and NIntegrate
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Sat, 6 Oct 2007 04:28:31 -0400 (EDT)
• References: <fe4tfg\$5h\$1@smc.vnet.net>

```mfedert at gmail.com wrote:
> Hi all,
>
> I have what is probably a very simple problem.  I want to find x which
> solves an equation of the form
>
> \integral f(x,y) dy = 0
>
> I have tried something along the lines of
>
> FindRoot[ NIntegrate[ f(x,y) , {y, -inf, inf} ], {x, x_0 } ]
>
> but it doesn't work ---- my theory being that NIntegrate tries to go
> ahead and do the numerical integration before it knows what x is equal
> to... which blows up  because the integrand is - as a function of x -
> non-numerical... Is there a way around this?  I'm sure there's some
> trivial modification I can make to get things working again.
>

Here's an example:

In:= integral[a_?NumericQ] := NIntegrate[Exp[a*x], {x, 0, 1}]

In:= FindRoot[integral[x] == 2, {x, 1}]
Out= {x -> 1.2564312086261675}

--
Szabolcs

```

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