Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss

how to solve integral equation

2 views
Skip to first unread message

ms...@duke.edu

unread,
Mar 25, 2005, 5:58:58 AM3/25/05
to
I have a function

fcn[x_,b1_,b2_]:= Integrate[Exp[-(b1 x1^3 + b2 x1)],{x1,0,x}]

For a given large x, and a given b2, I need to solve

fcn[xlarge,b1,b2given]==1

for b1.

Any help would be greatly appreciated.

Matt

Bob Hanlon

unread,
Mar 26, 2005, 2:41:04 AM3/26/05
to
fcn[x_?NumericQ,b1_?NumericQ,b2_?NumericQ]:=
NIntegrate[Exp[-(b1 x1^3+b2 x1)],{x1,0,x}];

With[{x = 100,b2=.1 },
FindRoot[fcn[x,b1,b2]==1,
{b1,.1}]]

{b1 -> 0.5961404931802724}

fcn[100,b1,.1]/.%

1.


Bob Hanlon

Janos D. Pinter

unread,
Mar 26, 2005, 2:42:35 AM3/26/05
to

Matt,

you can use e.g. NMinimize.

Example:
NMinimize[{0, N[fcn[10., b1, 5.]] == 1}, {b1}]
returns
{0., {b1 -> -0.052110648972416615}}

Regards,
Janos D. Pinter
PCS Inc.
E-mail: jdpi...@hfx.eastlink.ca
Web: www.pinterconsulting.com

At 06:48 AM 3/25/2005, you wrote:

>I have a function
>
>fcn[x_,b1_,b2_]:= Integrate[Exp[-(b1 x1^3 + b2 x1)],{x1,0,x}]
>
>For a given large x, and a given b2, I need to solve
>
>fcn[xlarge,b1,b2given]==1
>
>for b1.
>
>Any help would be greatly appreciated.
>
>Matt
>
>
>

>--
>No virus found in this incoming message.
>Checked by AVG Anti-Virus.
>Version: 7.0.308 / Virus Database: 266.8.1 - Release Date: 3/23/2005


--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.8.1 - Release Date: 3/23/2005

0 new messages