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?