In calculus, Cavalieri's quadrature formula, named for the seventeenth-century Italian mathematician Bonaventura Cavalieri, is the definite integral of x to the power n from 0 to a, equal to a to the power n plus one divided by n plus one, for any n greater than or equal to zero, along with its indefinite-integral and other equivalent forms. Together with the linearity of the integral, the formula makes it possible to integrate any polynomial, and the term quadrature is the traditional word for area, since the integral is interpreted geometrically as the area beneath the curve y equals x to the power n; two especially important historical cases are the quadrature of the parabola, for y equals x squared, known since antiquity, and the quadrature of the hyperbola, for y equals one over x, whose value is a logarithm.
Facts
Connections
Attributed To
Source Cavalieri's Quadrature Formula (Wikipedia)
In Branch
Source Cavalieri's Quadrature Formula (Wikipedia)
Is Kind Of Object
Sources
1. Cavalieri's Quadrature Formula (Wikipedia)
Lead section
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫ 0 a x n d x = 1 n + 1 a n + 1 n ≥ 0, {\displaystyle \int _{0}^{a}x^{n}\,dx={\tfrac {1}{n+1}}\,a^{n+1}\qquad n\geq 0,} and generalizations thereof.
In Branch: Calculus, Lead sentence
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫
Attributed To: Bonaventura Cavalieri, Lead
The case of higher integers was computed by Cavalieri for n up to 9, using his method of indivisibles (Cavalieri's principle).
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.