**Another in our WWWTF (What in the World Will I ever use This For?) series:**

**Math Concept**: Integration

Having spent multiple hours over the past week helping official oldest daughter of Env-Econ (OODEE) work through calculus problem after calculus problem in preparation for the pending AP exam, I thought it might be helpful to see how she might eventually move past solving math problems to applying the concepts. Right now I'm going to focus on integration, and hopefully later I will come back and talk about differentiation (seems backwards, but integration is fresh in my mind right now). In what follows, I assume a working knowledge of basic integral calculus--otherwise why would you care what you use this for?

As a reminder, a definite integral is defined as:

where f'(x) is the derivative of the function f(x) with respect to the variable x.

Graphically, the integral represents the area under the function y=f'(x) over the closed domain [a,b].

An example might help. Consider the simple linear function f'(x)=6-2X. What is the definite integral of f'(x) over the closed domain [1,3]?

What does this look like graphically?

Notice that for this case of a linear function (a line), the area under the function makes a triangle. A simple way to check your integration is to just find the area of the triangle on the graph.

The area of the triangle is .5(Base x Height) = .5(2 x 4) = 4. This is the same result we got for the intergral. For more complicated functions (non-linear), the area under the function isn't a nice neat geometric shape.

I know what you're thinking: Nice pictures and it's great fun to think about math, but WWWTF? (**W**hat in the **W**orld **W**ill I ever use **T**his **F**or?). Keep reading for an application to environmental economics.

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