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Multiple choice question


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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