Numerical integral

Numerical integral

Compare trapezoid, composite Simpson and adaptive Simpson estimates of ∫ₐᵇ f(x) dx. Blue shading is positive and orange shading is negative; the integral sums signed contributions, with reversed bounds changing the sign.

Choose boundary a or b, then click or drag in the graph. Release to recalculate. Even n controls the fixed grids; doubling n gives a scale-change diagnostic. Adaptive refinement uses a tolerance relative to sampled absolute mass, with bounded work.

Error indicators are estimates, not certified bounds. Narrow peaks or singularities between sampled points may be missed. Non-finite sampled values fail the calculation; improper integrals and principal values are not supported. A refinement-limit or roundoff warning means the adaptive estimate is unresolved.