Accumulation Functions
The AP Exam will also have problems that deal with accumulation functions. These are simply functions
of the form F(x) = f(t) dt. These are called accumulation functions because the value of the integral is
the area under the curve from the constant to the value x, and as x gets bigger, so does the area (it
“accumulates”). In these functions, t is a dummy variable that is used as the variable of integration.
Let’s do an example.
Example 1: Suppose we have the function F(x) = t dt. Let’s evaluate this at different values of x. First,
let’s find F(1). Graphically, we are looking for the area under the curve y = t from t = 0 to t = 1. It looks
like the following: