The derivative ( x n ) ′ = n x n − 1 {\displaystyle (x^{n})'=nx^{n-1}} can be geometrized as the infinitesimal change in volume of the n-cube, which is the area of n faces, each of dimension n − 1. Integrating this picture – stacking the faces – geometrizes the fundamental theorem of calculus, yielding a decomposition of the n-cube into n pyramids, which is a geometric proof of Cavalieri's quadrature formula.