Numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg78761] Numerical integration
- From: José Carlos Santos <jcsantos at fc.up.pt>
- Date: Mon, 9 Jul 2007 01:30:38 -0400 (EDT)
Hi all:
I detected a problem concerning numerical integration under Mathematica
5.1. Consider this function:
h[t_] := Exp[I t](Exp[I t] - 1)Sec[Exp[I t] - 1]
If I compute:
N[Integrate[h[t], {t, 0, 2Pi}]]
I get -3.58642. But if I compute
N[Integrate[Re[h[t]], {t, 0, 2Pi}] + Integrate[Im[h[t]], {t, 0, 2Pi}]I]
instead of getting the same answer, I get -9.869604401106042 +
2.2377264147293624^(-16)I. Of course, the imaginary part doesn't bother
me, but why are the results so different? BTW the difference is equal
to 2*pi.
Best regards,
Jose Carlos Santos