Re: How to NSolve equation which involves NIntegrate?

*To*: mathgroup at smc.vnet.net*Subject*: [mg120085] Re: How to NSolve equation which involves NIntegrate?*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 8 Jul 2011 04:51:01 -0400 (EDT)*References*: <201106250929.FAA20235@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

There are two solutions, by the way: Clear[f, g, a] f[a_] = Integrate[Sin[a x], {x, 0, 1}]; g[a_] = a*a; Plot[{a^2, f[a]}, {a, -.1, .6}] or Clear[f, g] f[a_?NumericQ] := NIntegrate[Sin[a x], {x, 0, 1}] g[a_] := a*a FindRoot[f[a] - g[a], {a, -.1}] FindRoot[f[a] - g[a], {a, 1}] {a -> 4.73799*10^-21} {a -> 0.490073} Bobby On Thu, 07 Jul 2011 10:40:10 -0500, DrMajorBob <btreat1 at austin.rr.com> wrote: > Clear[f, g] > f[a_?NumericQ] := NIntegrate[Sin[a x], {x, 0, 1}] > g[a_] := a*a > FindRoot[f[a] - g[a], {a, 1}] > > {a -> 0.490073} > > a) NumericQ eliminates the error you mentioned, > > b) NSolve is limited to algebraic problems, and > > c) I had to come up with a starting point for the search. > > (a) and (b) are related, in that NSolve wanted to keep a symbolic in > solving the problem, but f[a] is undefined, when a is symbolic. > > Bobby > > On Thu, 07 Jul 2011 09:58:23 -0500, Ted Sariyski > <tsariysk at craft-tech.com> wrote: > >> I am sorry, I should made up an example. Here it is: >> >> f[a_] := NIntegrate[Sin[a x], {x, 0, 1}] >> g[a_] := a*a >> NSolve[f[a] == g[a], a] >> >> Out[]: NIntegrate::inumr: "The integrand Sin[a x] has evaluated to >> non-numerical values for all sampling points in the region with >> boundaries {{0,1}}." >> >> Thanks, >> --Ted >> >> On 7/7/2011 10:26 AM, DrMajorBob wrote: >>> You left out the definition of h, so how can we possibly tell you why >>> it evaluates to non-numerical values? >>> >>> Bobby >>> >>> On Thu, 07 Jul 2011 06:31:38 -0500, Ted Sariyski >>> <tsariysk at craft-tech.com> wrote: >>> >>>> Hi, >>>> I need a numerical solution for a system of equations which involve >>>> numerical integrals. For one parameter the equation would be: >>>> >>>> f[a]==g[a] >>>> where >>>> f[a_]:=NIntegrate[h[x, a] , {x, x1, x2}] >>>> >>>> NSolve returns: "The integrand has evaluated to non-numerical >>>> values". >>>> >>>> Is there a built-in procedures for this type of problems or I need to >>>> make explicit iterations? >>>> >>>> Thanks in advance, >>>> --Ted >>>> >>>> >>>> >>>> >>>> >>> >>> >> > > -- DrMajorBob at yahoo.com