chensiyuan0510 发表于 2018-10-23 08:54 
y(x) is a function of x, so is p(x,t). Setting phi(x) as an indicater function only replaced phi(x ...
What about Dirac delta function, if you more familiar with this term. What I mean here is if we choose phi(x) in that way, then the integral of x will degenerate. But this is just my own opinion how we can reach (1.88) if all the previous derivations are correct.