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Solving an integral in the limit.

  • To: mathgroup at
  • Subject: [mg62389] Solving an integral in the limit.
  • From: Josef Karthauser <joe at>
  • Date: Wed, 23 Nov 2005 01:12:06 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I'm having trouble solving a complicated integral using mathematica,
and I'm looking for some wisdom on the matter.

The problem can be summarised as follows.  Mathematica can determine
the solution to,

    Integrate[E^(I*x^2)/ Sqrt[1 + x^2], {x, 0, Infinity}]

but if I replace the upper bound with a free variable and take the limit
as it goes to Infinity mathematica doesn't manage it,

    Limit[Integrate[E^(I*x^2)/ Sqrt[1 + x^2], {x, 0, a}], a -> Infinity]

Surely it should be able to determine that the answer is the same as in
the previous case.  Is there anyway to pursuade it?

Many thanks,
Josef Karthauser (joe at
FreeBSD (cvs meister, admin and hacker)
Physics Particle Theory (student)
================ An eclectic mix of fact and theory. =================

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