Multivariate Calculus

Chapter 8 Dirichlet's Theorem and Liouville'sExtension

8.1 Introduction

In this chapter, we will discuss two important theorems involving multiple integrals, viz., Dirichlet’s theorem and Liouville’s extension of Dirichlet’s theorem. We know that integrations are basically used for finding the areas of the two-dimensional regions and computing volumes of three-dimensional objects. Several physical applications of the definite integral are common in Engineering and Physics. The values of the integrals can be derived using various ways. In Chapter 6 and Chapter 7, we have considered and solved many such problems some of which can also be solved by using these two theorems, i.e., by Dirichlet’s theorem and Liouville’s theorem in comparatively ...