With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

18

Integrating functions of several variables

18.1 Elementary vector-valued integrals

We now consider the problem of integrating vector-valued functions of several variables. We begin by considering dissections, step functions and elementary integrals, as in the case of real-valued functions of a single variable. A cell C in Rd is a subset of Rd of the form I1 × · · · × Id, where I1, . . . , Id are intervals (open, closed, or neither) in R. Thus a one-dimensional cell is an interval and a two-dimensional cell is a rectangle. The d-dimensional volume or content vd(C) is defined to be .

Suppose that C = I1 × · · · × Id is a compact cell, and suppose ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required