       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.
>

```

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