Calculating the space a complex shape takes is hard, but it's not hard to calculate the space of a rectangle, so why not use smaller and smaller rectangles.

Join me as I re-invent integrals without realizing what I am doing.

@olafurw at least re-invent the trapezoid rule like Mary Tai.
Tai's model - Wikipedia

Apparently, Calculus Was Invented In 1994

A paper written in 1994 purports to develop a 'mathematical model for the determination of total areas under curves.'

Forbes
@olafurw
Can only not realize by never learning.
@olafurw This sounds more like the pre-calculus geometric appeal to infinitesimals. That they were able to produce answers in a simpler way than classic geometry was scandalous to some. Newton avoided geometric infinitesimals by inventing fluxions and thinking of things moving and time was divided into infinitesimals. Much less upsetting to the math conservatives.
@olafurw just make a perfectly proportioned solid stone carving of it and put it in water...
@olafurw I think it’s interesting how calculus seems more scary than it is (that we ended up using limits instead of infinititesimals probably didn’t help)

@olafurw

Now do Lebesgue integration.