Cavalieri's Quadrature Formula

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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/