Calculus
Integration by approximation
Trapezoids and Simpson's rule — when antiderivatives won't budge.
When an antiderivative isn't elementary, approximate the area numerically.
Common methods
- Rectangle (Riemann) — sum of f(xᵢ)·Δx.
- Trapezoidal — averages left and right rectangles.
- Simpson's — fits parabolas through triples; very accurate.