Math Playground
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.