シンプソンの公式（1/3・3/8）
シンプソンの1/3則および3/8則を用いて定積分を高精度に計算。合成公式の導出ステップ、打切り誤差評価、分割区間グリッド、曲線プロットグラフまで網羅。
Quadrature Parameters & Integrand
Variable: x
Quick test:
Supports powers (^), polynomials, exp, sqrt, sin, cos, ln, and constants (pi, e).
6 Panels
Step Size h = (b - a) / n: 0.166677 Evaluation Nodes
Target Tolerance Reverse Solver
Find the exact minimum number of subintervals (n) required to guarantee your desired precision.
Minimum Required Subintervals (n)4
Maximum Allowable Panel Width (h)0.25
Fourth Derivative Ceiling |f⁴(x)|: 1.197Guaranteed Truncation Bound: 2.5973e-5
Definite Integral Approximation0.341347Simpson's 1/3 Rule
Theoretical Error Bound |E|5.1304e-6O(h⁴) Truncation Ceiling
Richardson High-Precision Benchmark0.341345N=512 Extrapolated
Uniform Step Size (h)0.16667n = 6 Subintervals
Parabolic Osculating Curve Visualizer
Exact Function f(x)
Piecewise Simpson Parabolas
Evaluation Ordinates (xi, yi)
Quadrature Residual Area
Quadrature Execution Summary
Definite integral evaluation calculated via composite Newton-Cotes parabolic interpolation.
Applied Quadrature Formulation:Simpson's 1/3 Rule (Parabolic)
Total Subinterval Panels:6 panels
Total Evaluation Ordinates (n + 1):7 nodes
Panel Interval Width (h):0.166667
Algebraic Degree of Precision:Degree 3 (Exact for cubics & quadratics)
Richardson Benchmark Value:0.3413447
Absolute Error Deviation:2.0953e-6
Theoretical Convergence Order:O(h⁴) Quartic Convergence
Analytical Note: Because Simpson's 1/3 rule fits a symmetric second-degree parabola over pairs of panels, odd third-degree polynomial terms cancel out entirely, providing exact zero-truncation precision for any cubic curve ax³ + bx² + cx + d!
Current Integral0.341347
Error Ceiling5.1304e-6
Local Execution< 1 ms (Zero Float Drift)
Empathetic notice: Numerical quadratures approximate real-world curves by fitting smooth arches. Ensure your function has no infinite singularities within the boundaries for peak mathematical fidelity.
