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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: [mg46271] Re: how to explain this weird effect? Integrate
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Thu, 12 Feb 2004 22:47:07 -0500 (EST)
  • References: <c0ftbt$c7p$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

r = Integrate[Sin[m *  x] Sin[n * x], {x, 0, 2 Pi}];

You need to use a limit

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

Pi


Bob Hanlon

In article <c0ftbt$c7p$1 at smc.vnet.net>, nma124 at hotmail.com (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?


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