       Solving an integral in the limit.

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

```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,
Joe
--
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================ An eclectic mix of fact and theory. =================

```

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