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Riemann sums and the definite integral

Rectangles under a curve multiply from 1 to n; the running sum converges to the exact integral.

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720p preview, watermarked, no credits · About 34s

Live sketch. The film is rendered by Manim, with captions and motion.

Storyboard

  1. 01The region
  2. 02One rectangle
  3. 03Four rectangles
  4. 04Many rectangles
  5. 05The limit

Key values in the video

S_4
2.9766
S_32
3.6456
∫ f dx
15/4