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 **R**^{d} is a subset of **R**^{d} of the form *I*_{1} × · · · × *I _{d}*, where

Suppose that *C* = *I*_{1} × · · · × *I _{d}* is a compact cell, and suppose ...

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