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