Requires understanding of integrals.

Given the imprecise nature of the question, the moment mathematical precision was introduced, I became extremely skeptical this would be productive. I was not disappointed, though I understand the math well enough. My issue is not with your formulae but with their relevance.

The two biggest problems in analyzing the value of self-improvement are that we don't know what it's worth and, worse, it's endogenous - improving ourselves yields direct utility (if we value our "character," "virtue," or what-have-you), indirect utility (improving our ability to obtain additional goals), and may itself change our utility function (e.g. self-modifying to be a person who cares more about physical fitness has altered the coefficient of many junk foods in my utility function).

It's not wholly irrelevant, but the inputs are so ill-defined as to render formalizing it of no practical value.

I'm thinking of writing a sequel called When to Self-Improve in Practice

If this is an accurate description, I'd be very much interested in reading it.