Q:

NIntegrate & non-numerical values

I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. How can I change my code so that this is not an issue? A simple example is copied below.
a = 1/20; b = 1/5;
FF[y_] := Exp[I a y - 1/2 b^2 y^2];
f[x_] := NIntegrate[E^(-I x y) FF[y], {y, 0.0, 100}];
NIntegrate[f[x], {x, -100, 100}]

Thanks...

A:

a = 1/20; b = 1/5;
FF[y_?NumericQ] := Exp[I a y - 1/2 b^2 y^2];
f[x_?NumericQ] := NIntegrate[E^(-I x y) FF[y], {y, 0.0, 100}];
NIntegrate[f[x], {x, -100, 100}]

converges slowly ... to Pi

