The aim of this chapter is to study double- and triple integrals along with their applications. Thus, we shall consider here the integrals of the functions of two- and three variables.
9.1 DOUBLE INTEGRALS
The notion of a double integral is an extension of the concept of a definite integral on the real line to the case of two-dimensional space. Let f (x, y) be a continuous function of two independent variables x and y inside and on the boundary of a region R. Divide the region R into subdomains R1, R2,…, Rn of areas δR1, δR2,…, δRn, respectively. Let (xi, yi) be an arbitrary point inside the ith elementary area, δRi. Consider the sum
When n → ∞, the number of subregions increases indefinitely such that the largest of ...