Home | 18.022 | Chapter 11

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11.1 Introduction

Given a surface S or volume V and an integrand f(x, y, z), defined and reasonably well behaved in S or V, we can form the analogue of Riemann sums in this context.
For volume: break V up into small pieces and sum a value of f in each piece times  its volume; take the limit as the volumes of all pieces goes to zero in every possible way. If it exists this limit is the multiple integral of f over V. The limit can be shown to exist when f is continuous and V is compact (bounded and closed). It often exists otherwise as well.


Iterated integrals
Any product which contains two or more integrals in it can be considered an iterated integral.