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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



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