Skip to main content ☰ Contents You! < Prev ^ Up Next > \(\require{cancel}\newcommand{\dee}[1]{\mathrm{d}#1}
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Chapter 2 Applications of Integration
In the previous chapter we defined the definite integral, based on its interpretation as the area of a region in the \(xy\) -plane. We also developed a bunch of theory to help us work with integrals. This abstract definition, and the associated theory, turns out to be extremely useful simply because "areas of regions in the \(xy\) -plane" appear in a huge number of different settings, many of which seem superficially not to involve "areas of regions in the \(xy\) -plane". Here are some examples.
The work involved in moving a particle or in pumping a fluid out of a reservoir. See section
2.1 .
The average value of a function. See section
2.2 .
The center of mass of an object. See section
2.3 .
The time dependence of temperature. See section
2.4 .
Radiocarbon dating. See section
2.4 .
Let us start with the first of these examples.
