Area Under Curves

Thomas J. Pfaff ()
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Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 28 in Applied Calculus with R, 2023, pp 317-329 from Springer

Abstract: Abstract Up to this point we have developed techniques to extra information about curves related to their rate of change. We can now quantify how fast a curve is increasing or decrease, identify maximum and minimum points, and identify inflection points. There is still more valuable information in the graphs that we would like to quantify. For example, in the Function Gallery figure 3.8 has data and models to represent distribution of energy consumption in the U.S. and World. The line $$y=x$$ y = x would represent perfect equality of the distribution of energy. The area between the curve and $$y=x$$ y = x is used to quantify how much the given resource, in this case energy, deviates from equality; known as the Gini coefficient (technically the Gini coefficient is this area divided by 2). The problem now is how do we calculate this area? Here is another example.

Date: 2023
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DOI: 10.1007/978-3-031-28571-4_28

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