When I tried the integration of the Gaussian pdf function as attached to this message, Mathematica returns a result which is difficult to understand. Apparantly, the result should be 1.
It seems that Mathematica gives results for two cases of (1) Re(a^2)>0, and (2) otherwise.
My Question is:
(1) What is the exact meaning of the result of the integration as in the attached Gaussian.nb file?
(2) Can I define a variable to be a real number althrough I don't want to give it a numerical value? In the case of the attached integration, I'd like to let the software know that "a" is a real number before it starts to compute the integration.
Attachment: Gaussian.nb, URL: ,