Re: Assuming and Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg128325] Re: Assuming and Integrate
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 7 Oct 2012 01:30:54 -0400 (EDT)
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• References: <20121006055312.C0D5B6908@smc.vnet.net>

```f[m_, n_] = Assuming[Element[{n, m}, Integers],
Piecewise[{
{Integrate[Sin[n*x]*Sin[n*x], {x, 0, Pi}],
m == n},
{Integrate[Sin[n*x]*Sin[m*x], {x, 0, Pi}], m != n}}]]

Piecewise[{{Pi/2, m == n}}, 0]

f @@@ {{m, n}, {m, m}, {3, 2}, {3, 3}}

{Piecewise[{{Pi/2, m == n}}, 0],
Pi/2, 0, Pi/2}

Assuming[m == n, Simplify[f[m, n]]]

Pi/2

Bob Hanlon

On Sat, Oct 6, 2012 at 1:53 AM,  <hamiltoncycle at gmail.com> wrote:
> When I try the line below in Mathematica 8 I get the answer 0 which is what I expect when m and n are different but not when m=n. Can anyone explain how to do this correctly?
>
> Assuming[Element[{n, m}, Integers], Integrate[Sin[n*x]*Sin[m*x], {x, 0, Pi}]]
>
> When m=n we should get Pi/2, as in this case:
>
> Assuming[Element[n, Integers], Integrate[Sin[n*x]*Sin[n*x], {x, 0, Pi}]]
>
> cheers, Robert
>

```

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