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.

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 *R*_{1}, *R*_{2},…, *R*_{n} of areas δ*R*_{1}, δ*R*_{2},…δ*R*_{n}, respectively. Let (*x*_{i}, *y*_{i}) be an arbitrary point inside the *i*th elementary area, △*R*_{i}. Consider the sum

When *n* → ∞, the number of subregions increases indefinitely such that the largest ...

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