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