Chapter 7 Line, Surface and Volume Integrals
7.1 Introduction
In Chapter 6, the integrals of functions of several variables involving multiple integrals, i.e., double and triple integrals have been discussed in details. In this chapter, we shall study few new concepts of integrals - Line, Surface and Volume integrals and their interrelationship. We shall also discuss the applications of dou- ble and triple integrals over region, with line integrals over its boundary, referred to as Green’s Theorem (or Green’s Theorem in a plane), and can be generalized to cover Stoke’s Theorem and Gauss Divergence Theorem.
Roughly speaking, Line integrals are integrals of functions, defined over curves. In Riemann integral, it is known to us that the region ...
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