Deriving the Coefficients of Simpson's Rule in Calculus
Simpson's rule approximates the definite integral of a function over an interval by fitting a quadratic (parabola) through three equally spaced points on the curve and computing the exact area under that parabola in closed form; this derivation shows that the resulting area equals (h/3)(y0 + 4y1 + y2), which explains the origin of Simpson's rule's characteristic 1-4-1 coefficient pattern. This belongs to numerical integration within calculus, a topic concerned with approximating definite integrals of functions that may be difficult or impossible to integrate exactly.
Deriving the Coefficients of Simpson's Rule in Calculus
Simpson's rule approximates the definite integral of a function over an interval by fitting a quadratic (parabola) through three equally spaced points on the curve and computing the exact area under …