L'intégrale en 8 minutes.

Understand in 8 minutes what they don't say in class: The integral is the idea of ​​accumulation In this short video, we start with a simple idea: snow falls on the roof of a chalet, hour after hour. If we know the amount of snow falling at each moment, the integral allows us to determine how much snow has accumulated in total. The idea of ​​the integral, therefore, isn't primarily a complicated formula: it's the very physical concept of accumulation. We'll see why the integral corresponds to the area under the curve, first in the case of a constant function, then a piecewise constant function, before understanding how this idea generalizes to continuous functions. A Desmos table is also available for you to experiment and see in real time how the integral calculation is constructed. Objective: to get a head start on the final year curriculum with a concrete example, before the formulas. If you like this format, let me know with a like, a comment, or a subscription: it will encourage me to make more short videos like this. And if these videos are successful enough, I'll even provide you with free Anki flashcards to easily and permanently memorize everything, right on your phone. Coming soon: Darasa, my game for learning how to learn better. ///////////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////////////////////////////// --------------- Desmos Links: ----------------------------------------- As in the video: https://www.desmos.com/calculator/sbz... BONUS: Two snowfalls, one after The other one https://www.desmos.com/calculator/sbz... Large, stable cloud https://www.desmos.com/calculator/3zg... Large cloud Unstable https://www.desmos.com/calculator/y3f... ///////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////////////////////// Math in Brief Playlist:    • Math en Bref   #Maths #FinalYear #Integral #MathInBrief #MathMana Possible Chapters 00:04 — Snow on the Cabin 00:12 — Snow Amount Curve 00:22 — Snowfall Intensity Curve 01:20 — From Snowfall Intensity to Snow Amount 02:03 — The Idea of ​​Accumulation 02:41 — Integral and Area Under the Curve 03:50 — Constant Function: A Rectangle 04:39 — Step Function 04:56 — Continuous Function 05:30 — Integration Formula 06:30 — Desmos Graph 07:46 — Support Me! 08:01 — Darasa: The Video Game for Learning How to Learn 02:20 — The Area Under the Curve 03:10 — Piecewise Constant Functions 04:15 — Adding Rectangles 05:10 — Towards Continuous Functions 06:15 — The Integral as Accumulation 07:00 — Experimenting with Desmos 07:30 — Key Takeaways 07:50 — If You Like It 08:00 — Anki Cards 08:05 — Darasa, the Game for Learning How to Learn