# Difference between different approximations in QM and other definition of the integral

I am currently studying the path integral formalism by myself and I am a bit lost within all the different way to solve the integrals we have. I have one big question:

It sounds maybe a bit strange but I don't really see the conceptual difference between

Following me, the 4 methods are always approximating the integral thanks to a Taylor development to the second order in order to analytically solve the integral. Is there a difference of validity for these methods ( by that I mean one case where one method is a good approximation and not the others ).

I don't think I have a really good comprehension of these methods so excuse me if it is way off the mark.

• @Qmechanic aren't stationary phase and steepest descent literally the same thing? – DanielSank Mar 2 at 21:25