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Re: Solving an integral in the limit.

  • To: mathgroup at
  • Subject: [mg62417] Re: Solving an integral in the limit.
  • From: "Jens-Peer Kuska" <kuska at>
  • Date: Wed, 23 Nov 2005 06:27:28 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <dm11o7$e0s$>
  • Sender: owner-wri-mathgroup at


when the integrand is extended into the complex plane,
one may be able to compute the defined integral without
finding the undefined integral and take the limit.


"Josef Karthauser" <joe at> schrieb im 
Newsbeitrag news:dm11o7$e0s$1 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, 
| 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 
| Many thanks,
| Joe
| -- 
| 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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