Numerical Quadrature and Error Bounds — Cheat sheet

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Core rule

∣I−Tn∣≤M2(b−a)312n2,|I-T_n|\le\frac{M_2(b-a)^3}{12n^2}, ∣I−Sn∣≤M4(b−a)5180n4.|I-S_n|\le\frac{M_4(b-a)^5}{180n^4}.

Watch for

Simpson needs even nn on a uniform grid. Error bounds require the stated derivative bounds; sample agreement alone is no guarantee.