Introduction & Chapter Objectives

Introduction

Integration is one of the fundamental concepts in calculus and analysis. 
It allows us to compute quantities such as areas, volumes, lengths, and other accumulated measures. 
In this chapter, we first review the basic principles of the Riemann integral and the computation of simple integrals. 
We then extend these ideas to multiple integrals, which enable the evaluation of integrals over two or three-dimensional regions. 
These tools are essential in mathematics, physics, and engineering, as they provide the foundation for solving problems involving continuous quantities such as mass, charge, and energy distribution.

Chapter Objectives

At the end of this chapter, students should be able to:

    1.  Recall the definition of the Riemann integral and compute basic integrals.

   2.   Apply the properties of definite and indefinite integrals.

    3.  Evaluate double and triple integrals over different domains.

    4.  Use change of variables in multiple integrals (polar, cylindrical, and spherical coordinates).

    5.  Apply multiple integrals to compute areas, volumes, and other physical quantities.