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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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