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.

Mathematical Visual Proofs
51.6K views • Mar 20, 2025

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
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
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Video Information
Views
51.6K
Likes
3.1K
Duration
0:57
Published
Mar 20, 2025
User Reviews
4.7
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