Applications of the Definite Integral

Abstract

First we define the concepts of length, area, and volume: these geometric concepts are given analytic definitions using the concept of the definite integral which we have developed. We compute the arc length, the surface area, and the volume for some special cases, such as geometric figures produced by revolving one-dimensional curves in space. Then, the centroids of plane regions and curves, and the moments of curves and of solids are calculated. It is shown that the definite integral can be applied to the law of conservation of mechanical energy, to Einstein’s theory of relativity, and to calculate the escape velocity from the earth. At the end of the chapter, we consider examples connected with atomic energy, critical mass and atomic reactors.