Formula de cuadratura Simpson-Cavalieri

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Cezar Lupu
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Formula de cuadratura Simpson-Cavalieri

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Daca \( f:[a, b]\to\mathbb{R} \) este o functie de clasa \( C^{4}[a,b] \) atunci exista \( \xi\in (a, b) \) astfel incat

\( \int_{a}^{b}f(x)dx=\frac{(b-a)}{6}\left[f(a)+4f\left(\frac{a+b}{2}\right)+f(b)\right]-\frac{(b-a)^{5}}{2880}f^{(4)}(\xi). \)
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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