Uploaded February 2025 | Updated September 2026, 2 weeks ago
In this installment of synthwave and math, we sketch the net accumulation curves of elementary functions by measuring the directed, signed area between the curve and the x-axis. This means that area above the x-axis, moving from left to right, is positive. If you move from right to left it is negative, and then these switch below the x-axis. We use these accumulation functions to state general antiderivative rules. Along with various rules (like substitution and integration by parts, etc.) and chain rules, these rules help you find a variety of antiderivatives. If you want proof that these are the correct derivatives, you should consult any standard calculus text.
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Thanks!
For a related video with derivatives, check out:
youtu.be/Ud_aN6TXuhk
For more math and synthwave, check out:
youtube.com/playlist?list=PLZh9gzIvXQUsNIO0jVHE6kTkH0Q6IFJ1R&si=jieXuCRDmsssxD93
#manim #calculus #derivative #antiderivative #integral #powerrule #trigonometry #sine #cosine #mathvideo #math #mtbos #animation #iteachmath #mathematics #enumeration #synthwave #naturallog #exponential #derivativerules #differentialcalculus
To learn more about animating with manim, check out:
https://manim.community
______________________________________
Music in this video:
Our Sunrise by Diamond Ace | soundcloud.com/diamond-ace-music
Music promoted by free-stock-music.com
Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
creativecommons.org/licenses/by-sa/3.0/deed.en_US
In this installment of synthwave and math, we sketch the net accumulation curves of elementary functions by measuring the directed, signed area between the curve and the x-axis. This means that area above the x-axis, moving from left to right, is positive. If you move from right to left it is negative, and then these switch below the x-axis. We use these accumulation functions to state general antiderivative rules. Along with various rules (like substitution and integration by parts, etc.) and chain rules, these rules help you find a variety of antiderivatives. If you want proof that these are the correct derivatives, you should consult any standard calculus text.
If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at buymeacoffee.com/VisualProofs
Thanks!
For a related video with derivatives, check out:
youtu.be/Ud_aN6TXuhk
For more math and synthwave, check out:
youtube.com/playlist?list=PLZh9gzIvXQUsNIO0jVHE6kTkH0Q6IFJ1R&si=jieXuCRDmsssxD93
#manim #calculus #derivative #antiderivative #integral #powerrule #trigonometry #sine #cosine #mathvideo #math #mtbos #animation #iteachmath #mathematics #enumeration #synthwave #naturallog #exponential #derivativerules #differentialcalculus
To learn more about animating with manim, check out:
https://manim.community
______________________________________
Music in this video:
Our Sunrise by Diamond Ace | soundcloud.com/diamond-ace-music
Music promoted by free-stock-music.com
Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
creativecommons.org/licenses/by-sa/3.0/deed.en_US
