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Re: Re: Re: Trouble with Integrate


Marko Vojinovic <vojinovi at panet.co.yu> wrote on Tue, 11 Feb 2003 04:41:28

MV> Let

MV> g = Sqrt[1+x^(2a)]-x^a

MV> where if we put the parameter a to be 2 we recover the original function, f.
MV> Now,

MV> Integrate[g,{x,0,Infinity}] /. a->2

MV> gives the correct answer


In[1] := Integrate[Sqrt[1 + x^(2a)] - x^a, {x, 0, Infinity}] /. a -> 2/3

Out[1] = -(Gamma[-5/4]*Gamma[7/4])/(2*Sqrt[Pi])   (*  <- INVALID  *)

In[2] := N[%]

Out[2] = -1.01666


Actually this integral, obviously, diverges to the plus infinity.

In[3] := N[Integrate[Sqrt[1 + x^(2a)] - x^a, {x, 0, 10^10}] /. a -> 2/3]

Out[3] = 3232.


Best wishes,

Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group

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