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MathGroup Archive 2004

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Re: how to explain this weird effect? Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46261] Re: how to explain this weird effect? Integrate
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 12 Feb 2004 22:46:24 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <c0ftbt$c7p$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Limit[Limit[r, n -> m], m -> 2]

Regards
  Jens

steve_H wrote:
> 
> I type:
> 
> r = Integrate[Sin[m  x] Sin[n x], {x, 0, 2 Pi}]
> 
> then I type
> 
> r /. {n -> 2, m -> 2}
> 
> I get error (1/0 expression encountered) and no result.
> 
> but when I let m=2 and n=2 right into the integral first, it works:
> 
> r = Integrate[Sin[2 x] Sin[2 x], {x, 0, 2 Pi}]
> 
> and I get Pi as expected.
> 
> I wanted to integrate this once, and try the output for different n,m.
> 
> I did not think it will make a difference as to when I replace m and n
> by their numerical values, but Mathematica disagrees.
> 
> I know Mathematica is correct in this, since it is clear from the result
> of the integration why I get 1/0. But it seems to me I should
> get the same result if I replace m,n inside the integral before
> the integration operation starts, or replace them afterwords.
> 
> For example, when I type
> 
> Integrate[Sin[m x], {x, 0, Pi}]
> % /. m -> 4
> 
> I get zero.
> 
> and when I replace m with 4 inside the integral first, I get the same
> result as above:
> 
> Integrate[Sin[4 x], {x, 0, Pi}]
> 0
> 
> So, what do you think? is there something I am missing here?
> 
> thanks
> Steve


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