Understanding the Fundamental Theorem of Calculus Part 2 📐

Explore a quick animation that proves the second part of the Fundamental Theorem of Calculus, revealing how it links differentiation and integration through the concept of signed area.

Understanding the Fundamental Theorem of Calculus Part 2 📐
Mathematical Visual Proofs
51.6K views • Mar 20, 2025
Understanding the Fundamental Theorem of Calculus Part 2 📐

About this video

This short animation uses the first part of the fundamental theorem of calculus to prove the second part. In particular, it shows that the signed area between a curve and the x-axis over an interval can be computed by taking the difference of any antiderivative of the curve evaluated at the two interval endpoints.

For part one visual proof, see https://youtube.com/shorts/BbCEv6L9_oA?si=rmTAFbFcunkqk5zp



If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at https://www.buymeacoffee.com/VisualProofs
Thanks!


#manim #calculus #derivative #antiderivative #integral # #mathvideo​ #math​ #mtbos​ ​ #animation​​​ #iteachmath #mathematics #derivativerules #differentialcalculus #fundamentaltheoremofcalculus #theorem #area #accumulation

To learn more about animating with manim, check out:
https://manim.community

Tags and Topics

Browse our collection to discover more content in these categories.

Video Information

Views

51.6K

Likes

3.1K

Duration

0:57

Published

Mar 20, 2025

User Reviews

4.7
(10)
Rate:

Related Trending Topics

LIVE TRENDS

Related trending topics. Click any trend to explore more videos.