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