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Engineering Mathematics, Volume I, Second Edition by Babu Ram

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12

Multiple Integrals

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.

12.1 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, △Ri. Consider the sum

 

 

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

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