January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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5.34 Double Integrals
A double integral is used to calculate the area under a surface over a bounded region.
In order to approximate the volume under a surface over a domain D, the domain
can be divided into rectangles. Each of these rectangles has an x and a y dimension
denoted as Δx and Δy, respectively. Therefore, the area of each rectangle is defined
as ΔA 5 ΔxΔy.
To obtain the actual volume under a surface, the partitions of the domain must
be made infinitely small by finding the infinite limit of the double summations
in the volume approximation. As this limit approaches infinity, the error of the
approximation approaches 0.
V 5 lim
m!N
lim
n!N
X
m
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