229807a2-ac34-4c5c-9fa3-8a04cda261eb 5 4 5 decimal

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Adaptive recursive quadrature based on the Simpson Rule for the calculation of integrals

t0 1 time :

f a b N ε ∫AdapRecursive I.0 b a - 6 / a f 4 a b + 2 / f * + b f + (* : ε 10 ε * : f a b N ε I.0 Recursive eval 31 line eval :

f a b N ε I.0 Recursive N 0 ≡ I.0 Number of Iterations exceeded : c a b + (2 / : I.1 c a - 6 / a f 4 a c + 2 / f * + c f + (* : I.2 b c - 6 / c f 4 c b + 2 / f * + b f + (* : I.0 I.1 - I.2 - abs ε > I.0 f a c N 1 - ε 2 / I.1 Recursive f c b N 1 - ε 2 / I.2 Recursive + : I.0 I.1 I.2 + : if 41 line if I.0 21 line :

t0 1 time :

Function x f x sqrt exp :

Number of iterations N 1000 :

Precision ε 0.000000001 :

Lower Limit a 0 :

Upper Limit b 2 :

f a b N ε ∫AdapRecursive 5.40752818445865

1 time t0 - min 0.0097

x f

x sqrt exp x a b int 5.40744702348009