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Multiple choice question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26677] Multiple choice question
*From*: F.H.Simons at tue.nl
*Date*: Wed, 17 Jan 2001 00:47:27 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
We compute an integral in four different ways (one numerically and three
symbolically). Which of the following results is correct?
In[12]:=
NIntegrate[ Exp[I t 2 ]/(t-1-I), {t, 0, Infinity}, Method->Oscillatory]
Out[12]=
-0.934349-0.70922 I
In[13]:=
Integrate[ Exp[I t 2 ]/(t-1-I), {t, 0, Infinity}] // N
Out[13]=
-0.547745-0.532287 I
In[14]:=
N[Integrate[ Exp[I t u ]/(t-1-I), {t, 0, Infinity}] /. u-> 2]
Out[14]=
-0.16114-0.355355 I
In[15]:=
N[ Integrate[#, {t, 0, Infinity}]& /@ ComplexExpand[ Exp[I t 2 ]/(t-1-I),
TargetFunctions->{Re, Im}] // Expand ]
Out[15]=
-0.724677-0.145683 I
(And why are the other results false?)
Fred Simons
Eindhoven University of Technology
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