I made this tutorial about how to find the rocket equation using calculus. Now I know that it seems outside of my normal area of interest, but the truth is that I have a secret love of mathematics. I solve physics problems for the same reason people like doing puzzles; for an entertaining challenge. Anyway, I digress.
There are two things discussed here. First is the indefinite integral which gives a function of the rocket’s speed with respect to time, and secondly is the definite integral, which gives the rocket’s change in speed or ‘delta v.’
I started with acceleration instead of the other approaches because it’s intuitive if you understand Newton’s equations pretty well. I also made a graph on desmos with all three integrations from acceleration to position graphed out as functions of time.