So I am reading the proof for the integral formula for the length of any curve from a to b. What I don't understand:
I understand how delta x is extracted out from the expression algebraically. But the definition of a limiting sum is this:
Therefore by this definition the very first line of the working in the first photo, there ought to be a delta x in the first place. But there isnt. The only delta X terms I see are just contained within the corresponding f(x) part of the limiting sum definition. What? Why?