Simpson's First Rule - Area Integrator
Compute area under a curve sampled at three equally-spaced ordinates using Simpson's first rule - the building block for every naval-architecture volume, area and centroid integration.
Area
13.333m²
Formula, assumptions, and limits
Simpson-1 exact for polynomials up to order 3. For more than 3 ordinates extend as composite: A = h/3·(y₀ + 4y₁ + 2y₂ + 4y₃ + … + y_n). Number of intervals must be even.
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| Ordinate at station i | m | body plan | |
| Common interval | m | station spacing |