Re: Find value of unknown const that causes integral to
- To: mathgroup at smc.vnet.net
- Subject: [mg110326] Re: Find value of unknown const that causes integral to
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 13 Jun 2010 04:11:51 -0400 (EDT)
f[x_] = Integrate[BesselI[0, x*t], {t, 0, 1}]
HypergeometricPFQ[{1/2}, {1, 3/2},
x^2/4]
Plot[f[x], {x, -3, 3},
PlotRange -> {0, 2}]
FindRoot[f[x] == 3/2, {x, 1}]
{x->2.23039}
f[x] /. %
1.5
Bob Hanlon
---- Jason Quinn <jason.lee.quinn at gmail.com> wrote:
=============
Suppose I have an expression of the form
1/2 = int_0^1 besselI[0,x*t] dt
and I want to find the value of "x" that will make the integral true.
Can Mathematica handle such situations? I've tried all the main
suspects that I get warnings that the expression depends on x in a non-
algebraic way. The numerical tasks do not seem to work either. The
expression above is just a made-up example, but in general, what do to
when you are trying to solve equations of this type? I could
certainly write a function that find the value iteratively myself, but
I'd be surprised if such a thing doesn't already exist.
Cheers,
Jason
PS I've tried Wolfram Alpha and
solve 1 = int besselI0(x*t) from t=0 to 1
fails but
solve 1/2 = int erf(x*t) from t=0 to 1
works.
--
Bob Hanlon