Wow😲! The visual explanation of integration in calculus.

This is a Reimann sum, and has been the basic introduction to integral calculus for as long as I can remember. It's how I was introduced to integrals over 40 years ago. The visual explanation is in almost every calculus textbook.

Forty-year-old animation. Still clearer than most modern lectures. That should bother us a little.

The Mechanical Universe series, one of my favorite inspirations. Limit for integration approaches the indeterminate form ∞ • 0 For Derivatives the limit approaches the indeterminate form 0 / 0 Indeterminate Forms are Specific Mathematical Singularities.

This is Riemann Integral. Not Lebesgue's

I finally understood integrals when I realized that the volume of a sphere is the integral of the surface of a circle

This reminds me on Riemann sum in James Stewart Calculus early transcendental

We stand on the shoulders of giants.

Math was never a strong suit for me. What I heard was "Blah, blah blah and something else". It did remind me of this though:

awful visualization though

Two figures in a textbook accomplishes that very well.

The “as x approaches zero” function is one of rhe coolest math insights (was it Newton?)

Pretty much how I learned it in school here in Italy. I'm curious about how have you been taught about integrals around the world?

That's awesome. Mathematics is the language of nature. The more we observe nature and visualize it the more we can analyze it using mathematics.

Todos rectagulitos chiquititos, tan chiquitito que no se ven y los sumas.

what documentary is it? thank you.

The Mechanical Universe! It was produced at Caltech. Each lecture in Physics 1 would feature one of these videos, an experiment & a lecture. Fantastic course. My freshman advisor was the mathematician on this series.

~ 😛🫦🤩

Differentiation animation??

This is exactly how it’s taught in Cal 1 btw

What video is this

Thank you

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God i hate Riemann sums

never seen somthing like that, crazy

If Riemann watched it he would have an overflow of bile…

Visual representation always makes things much easier for the learners. It’s awesome to understand the concept in few seconds.

You wont believe this, but I have an audiobook about calculus (from The Great Courses series).

Surely that was obvious?

that's Riemann integration

Totally agree — these visuals have been around for a long time. If you’re interested, we put together a learning plan that goes deeper, with much finer-grained concepts to help students bridge intuition and rigor.

Its an elephant

Respect to people who get it. Not me.

Why can’t we get updated calculus programs? Web assign is terrible and the videos are from the 80s lmao

This is explained (better) in literally every calculus textbook in the galaxy, since probably, Riemann.