Fundamental Theorem of Calculus Part 2 @MathVisualProofs

Uploaded March 2025 | Updated September 2026, 2 weeks ago

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 youtube.com/shorts/BbCEv6L9_oA?si=rmTAFbFcunkqk5zp

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

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$Building the Wallis Sieve: What’s the Area? In this short, we show how to build the Wallis Sieve using an iterative procedure of cutting remaining square lengths into the next odd and removing the created central square in the corresponding square grid. The question is: can you determine the area of the resulting limiting shape? If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Wallis Sieve, check out this wonderful short article by Evelyn Lamb: https://www.scientificamerican.com/blog/roots-of-unity/a-few-of-my-favorite-spaces-the-wallis-sieve/ If you want to see the area computed in terms of the infinite Wallis product, check out this short : https://youtube.com/shorts/s1JORwIzabs?feature=share #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #dynamicalsystems #fractal #fractals #wallissieve #wallis #wallisproduct #infiniteproduct To learn more about animating with manim, check out: https://manim.community$

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