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. Wikipedia