Cavalieri's quadrature formula
Mathematical term in calculus / From Wikipedia, the free encyclopedia
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In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral
and generalizations thereof. This is the definite integral form; the indefinite integral form is:
There are additional forms, listed below. Together with the linearity of the integral, this formula allows one to compute the integrals of all polynomials.
The term "quadrature" is a traditional term for area; the integral is geometrically interpreted as the area under the curve y = xn. Traditionally important cases are y = x2, the quadrature of the parabola, known in antiquity, and y = 1/x, the quadrature of the hyperbola, whose value is a logarithm.