// multi-utility computation suite · offline · instant · precise
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math.numerical-integration-gauss Calculator
Approximates a definite integral using Gaussian quadrature with 2, 3, or 5 nodes, achieving high accuracy with few function evaluations. Gaussian quadrature with n points is exact for polynomials of degree 2n−1 — it dramatically outperforms equally-spaced methods.
Inputs
Lower Limit A
Reference formula or conversion factor shown for context.
Upper Limit B
Reference formula or conversion factor shown for context.
N Points
Reference formula or conversion factor shown for context.
K Value
Reference formula or conversion factor shown for context.
Results
numerical integral (3-pt GL)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
exact integral (e^kx)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
absolute error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
3-point GL exact for polynomials
Sample size or count used in the calculation.
comparison with Simpson 1/3
Sample size or count used in the calculation.
Gauss-Legendre weights sum to
The computed weight (gravitational force) or mass.