John D. Cook • 6/4/2026

Integrating smooth periodic functions

This article examines the function f(x) = cos(sin(x) + x), a smooth periodic function with period 2π. It discusses how the trapezoid rule, which typically has error on the order of 1/N², performs exponentially better for such functions, achieving floating-point precision with only 16 integration points. The post provides error bound calculations and highlights the theoretical basis for this efficiency, making it relevant to numerical analysis and computational mathematics within the IT/technology domain.

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#floating-point #Error Analysis #Trapezoid Rule