Re: Find value of unknown const that causes integral to equal some

*To*: mathgroup at smc.vnet.net*Subject*: [mg110322] Re: Find value of unknown const that causes integral to equal some*From*: Peter Pein <petsie at dordos.net>*Date*: Sun, 13 Jun 2010 04:11:08 -0400 (EDT)*References*: <huvk44$rpa$1@smc.vnet.net>

There is no real-valued solution; to get complex solutions, try to give a complex value as starting point for FindRoot: target[x_?NumericQ] := NIntegrate[BesselI[0, x*t], {t, 0, 1}] and FindRoot[target[x]==1/2,{x,1+I}] {x->0.+2.84653 I} give what you want? Am Sat, 12 Jun 2010 09:30:44 +0000 (UTC) schrieb Jason Quinn <jason.lee.quinn at gmail.com>: > 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. >