Applications of the Fundamental Theorem

Abstract

Although the area beneath a curve is the simplest intuitive interpretation of the limit definition of the definite integral, there are many other physical quantities which may be so defined. Whenever a summation over small elements is indicated by the physical situation, we arrive at a definite integral on passing to the limit. In order to evaluate the definite integral we first try to find the anti-derivative by the techniques of formal integration, such as those outlined in the previous section, and then we apply the fundamental theorem.