Cavalieri's Quadrature Formula

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The definite integral

$int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1,$

(1)

where , , and are real numbers and is the natural logarithm.

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absolute value
definite integrals
{1/4, -1/2, 1} cross {1/3, 1, -2/3}

References

Bradley, D. M. "A Remark on Cavalieri's Quadrature Formula." Amer. Math. Monthly 110, 437, 2003.Wildberger, N. J. "A New Proof of Cavalieri's Quadrature Formula." Amer. Math. Monthly 109, 843-845, 2002.

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Cavalieri's Quadrature Formula

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Weisstein, Eric W. "Cavalieri's Quadrature Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CavalierisQuadratureFormula.html

Cavalieri's Quadrature Formula

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References

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