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Lizzie Wagner
Calculating Mass and Centroids Through Double Integration
Applying multiple integration is a useful technique for computing the area, volume,
mass, or the location of center of mass of a given region.
When solving for mass, the
appropriate form of integration is known as “double integration”. This is necessary because
any given region must have at least two dimensions to integrate over.
Finding mass through integration at first seems difficult.
But, by breaking the
process down into steps and understanding each of those steps thoroughly, what looks like an
impossible task is finally seen as an easy calculation.
In order to setup a system for
integrating with respect to mass, it is imperative that one first comprehends the terminology.
To solve for mass the key terms to learn are density, lamina, area, and region.
When a
problem refers to a “lamina with uniform density”, it means that the space that is being
integrated over is a thin platelike region that has the same concentration of mass per unit
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 Winter '08
 Boeri
 Multivariable Calculus

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