Re: Condition Generation in Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg126468] Re: Condition Generation in Integrate*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sat, 12 May 2012 04:56:36 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205110413.AAA23678@smc.vnet.net>

It is just a limiting case expr1 = Cos[Pi x]^2 Sin[Pi x (m+1)] Sin[Pi x (n+1)]; expr2 = Integrate[expr1, {x, 0, 1}]; expr3 = Simplify[Limit[expr2, m -> n+2], Element[n, Integers]] 1/8 expr4 = expr1 /. m -> n+2; expr5 = Simplify[Integrate[expr4, {x, 0, 1}], Element[n, Integers]] 1/8 Bob Hanlon Sent from my iPhone On May 11, 2012, at 12:13 AM, Michael Musheghian <michael.musheghian at gmail.com> wrote: > Greetings! > > Integrate[ > Cos[\[Pi] x]^2*Sin[\[Pi] x (m + 1)]*Sin[\[Pi] x (n + 1)], {x, 0, 1}] > > When I evaluate this I get an answer, however, there are some special case s (for example, m & n are both integers and m == n+2)in which this integral must yield different result. My question is, why doesn't it take in consideration all cases and doesn't generate conditional expressions? > > Thank you. >

**References**:**Condition Generation in Integrate***From:*Michael Musheghian <michael.musheghian@gmail.com>