Simpson’s Rule Works on ANY Function… So Why Is It Exact for Cubics

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Simpson's Rule is one of the most famous numerical integration techniques, but most people don't know why it is exact for cubics.

The secret lies in the fourth derivative. When the fourth derivative is zero, Simpson's error term disappears completely, making the approximation exact.

In this animation we compare cubics, quartics, quintics, sine functions, and exponentials to reveal the hidden mathematics behind Simpson's Rule.

Attributions:
1.Music track: Cozy Lofi Background Music for Relax, Study & Sleep
DesiFreeMusic
Source: https://pixabay.com/music/lofi-cozy-lofi-background-music-for-relax-study-amp-sleep-453302/

Видео Simpson’s Rule Works on ANY Function… So Why Is It Exact for Cubics канала AJ Tutoring Specialists - Maths Behind Everything