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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110289] Find value of unknown const that causes integral to equal some value
  • From: Jason Quinn <jason.lee.quinn at gmail.com>
  • Date: Sat, 12 Jun 2010 05:30:49 -0400 (EDT)

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.


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