This document provides an introduction to using definite integrals to calculate volumes, lengths of curves, centers of mass, surface areas, work, and fluid forces. It discusses calculating volumes through slicing solids and rotating areas about an axis. Examples are provided for finding the volumes of pyramids, wedges, and solids of revolution. It also discusses using integrals to find curve lengths, circle circumferences, and moments and centers of mass for various objects. Surface areas of revolution and fluid pressures are also explained.