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The integrand has evaluated to non-numerical values for all

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83838] The integrand has evaluated to non-numerical values for all
  • From: Kreig Hucson <kreig.hucson at yahoo.com>
  • Date: Sun, 2 Dec 2007 04:06:28 -0500 (EST)

Hi all,

Being given the function: 

f[x_,y_]:= Sin[x*y]*Exp[-(y-1)^2]/(x*y) ,
 
I want to integrate it with respect to y, from 0 to Infinity, and to obtain a function of x only, F[x].

I typed the command:

F[x_]:= Assuming[x>0, Integrate[f[x,y],{y,0,Infinity}]]

but the integral remained unevaluated by Mathematica 6.

After this, I typed the command:

F[x_]:= Assuming[x>0, NIntegrate[f[x,y],{y,0,Infinity}]]

but I received the error message: "The integrand f[x,y] has evaluated to non-numerical values for all sampling points in the region with boundaries {{Infinity,0.}}".
I looked at the explanations of the error message and there it was suggested to give a particular value to x and to compute the integral for that particular value. I gived one particular value and I obtained the expected result. Anyway I need to obtain an analytical expression for all x>0.
 
   My question is, how can be performed the integral and to obtain the analytical function F[x]?

  Thank You in advance,

  Kreig


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