Work out simpson rule instantly with clear inputs, formula shown and shareable results.
Simpson's rule fits a parabola through each pair of intervals, weighting the ordinates 1, 4, 2, 4, …, 4, 1. It is exact for cubics and its error falls as h⁴, far faster than the trapezoid rule's h².
Simpson's rule
∫ ≈ (h/3)[f₀ + 4f₁ + 2f₂ + 4f₃ + … + 4fₙ₋₁ + fₙ]
The exact value is 32/5 = 6.4 and Simpson gives 6.4000651 — an error of only 0.00007.
Each parabola spans two intervals, so an odd count would leave one unpaired.