5 - The Integral

Abstract

This chapter discusses integrals. Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. The theorem linking these concepts together is called the fundamental theorem of calculus. This theorem simply asserts that a definite integral can be calculated by evaluating any antiderivative at the endpoints of the interval of integration and then subtracting. There are two types of integrals: definite and indefinite integrals. The problem of finding a definite or indefinite integral is solved if an antiderivative for the function f can be found. However, this task can be often difficult. There are many other functions for which indefinite integrals can be found, but learning to recognize them takes a lot of experience.