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Re: Multiple choice question


Since the integral in question can alternatively
be calculated as:

In[1]:=
Limit[-Exp[-z] ExpIntegralEi[z] /. z->(e-I 2)(1+I), e->0] // N

Out[1]:= -0.547745-0.532287 I  ,

Out[13] (lucky 13!) seems to be valid.

Adam

F.H.Simons at tue.nl wrote:
> 
> 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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