Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

Numerical Methods for Approximating Definite Integrals: Simpson's Rule

Quick fact

Simpson's rule is so effective that for many functions it gives exact results for polynomials up to degree 3, while the trapezoidal rule is exact only for linear functions.

Why this is interesting

If a function has no elementary antiderivative, how can we still find the area under its curve? Simpson's rule provides an elegant numerical shortcut that often gives astonishingly accurate results.