The strange behaviour of NIntegrate
- To: mathgroup at smc.vnet.net
- Subject: [mg53508] The strange behaviour of NIntegrate
- From: Zaeem Burq <Z.Burq at ms.unimelb.edu.au>
- Date: Sat, 15 Jan 2005 01:44:07 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Dear all,
I'll describe the problem briefly first as follows:
I am trying to NIntegrate a nice function (which I know is integrable), of
the form
K[s] = h[s]/[(1-s)^1.5] from 0 to 1.
The function is real, but Mathematica spits out a COMPLEX answer!!
Admittedly, the complex part is very small, and if I truncate the integral
just below 1, the complex bit disappears and changes the real part very
slightly.
It seems obvious that Math'ca is choosing the last s value just beyond 1,
producing the Sqrt of a negative number in the denominator.
If interested, here are the calculations and results. Read on if you think
you can help. Thanx.
\!\(\(\[CurlyPhi][
x_] := \[ExponentialE]\^\(\(-x\^2\)/2\)\/\@\(2 \[Pi]\);\)\n
\(K[s_] := \(\(\ \)\(\((1 - \@s)\)\ \[CurlyPhi][\(1 - \@s\)\/\@\(1 -
s\)]\)\
\)\/\((1 - s)\)\^1.5`;\)\)
NIntegrate[K[s], {s, 0, 1}]
gives \!\(\(\(0.4206155890394436`\)\(\[InvisibleSpace]\)\) -
3.304807577181973`*^-49\ \[ImaginaryI]\)
and
NIntegrate[K[s], {s, 0, .999999}]
results in
0.420217
Any thoughts?
Zaeem.
Zaeem Burq
PhD Stochastic Processes,
Dept. of Mathematics and Statistics,
Unimelb.
Room 201, Richard Berry Building
University of Melbourne,
Parkville, VIC 3052.
ph: 8344 4248.
http://www.ms.unimelb.edu.au/~zab
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