Concepts without words: Integration and Riemann Sums 🟨🟩🟦 (by Mathematical Etudes) #math #science #iteachmath #mtbos #visualization #elearning #calculus

when you realize the calculation of an area is a finely estimated averaging operation; and then realize all of calculus is about the differential as an averaging tool (Δx is an expectation). Then stochastic calculus won’t seem so odd after all.

Meh, the real integration would be divide the figure into 4 squares and calculate the integral of each of the new 4 functions.

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What is going on here? Are we integrating an indicator function f(x,y) that is 1 if (x,y) in the figure, 0, if not, and what is being visualized is lower and upper darboux sums for progressively finer rectangular meshes? Only know defs for integrating on closed intervals of R

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