       fundamental Integrate question

• To: mathgroup at smc.vnet.net
• Subject: [mg73031] fundamental Integrate question
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Tue, 30 Jan 2007 06:44:16 -0500 (EST)

```Consider the classical example that incorrectly gave zero in a prior
version of Mathematica

In:=
Integrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]
Chop[N[%]]
Chop[NIntegrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]]

Out=
2*I*Pi

Out=
6.283185307179586*I

Out=
6.2831853071795685*I

Of course the result is correct considering the pole at origin and the
Residue theorem.

Trying to understand how Mathematica applies the Newton-Leibniz
formula I just want to know if
I am right below:

In:=
((F[z] /. z -> 1 - I) - F[z] /. z -> -1 - I) + ((F[z] /. z -> 1 + I) -
F[z] /. z -> 1 - I) +
((F[z] /. z -> -1 + I) - F[z] /. z -> 1 + I) + (Limit[F[z], z -> -1,
Direction -> -I] - F[z] /. z -> -1 + I) +
((F[z] /. z -> -1 - I) - Limit[F[z], z -> -1, Direction -> I])

Out=
2*I*Pi

Thanks for any response!

Dimitris

```

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