Integration in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg92123] Integration in Mathematica
• From: sigmundv at gmail.com
• Date: Sat, 20 Sep 2008 05:02:00 -0400 (EDT)

```Dear group,

Let

f[n_]:= Sin[Pi x] Cos[Pi x] Sin[n Pi x];

We then want to integrate f[n] w.r.t. x from 0 to 1 and therefore
issue the command

Integrate[f[n],{x,0,1}]

which yields

Sin[n Pi]/((-4 + n^2) Pi)

If we assume that n is an integer, the result is 0.

However, for n=2, the result above is not defined but nevertheless

Integrate[f[2],{x,0,1}]

returns 1/4, which is correct. In fact, n=2 is the only integer for
which the integral of f[n] is different from 0.

This leads me to ask if Mathematica should be able to single out the
case n=2 automatically, or if it at all would be able to. Of course,
the result Sin[n Pi]/((-4 + n^2) Pi) should lead you to examine the
case n=2 closer, but if you in advance told Mathematica to assume that
n is an integer, you would just get a plain 0 as a result.

What are your thoughts on the example above?

Regards,
Sigmund Vestergaard

```

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