1. Section 5.2 Accumulation Functions
MAT 213 Brief Calculus
Section 5.2
Accumulation Functions

2. The Accumulation Function F(x)
The accumulation function of a function f(t) ,
gives the accumulation of the area between the horizontal axis and the graph of f from a to x.
The constant a is referred to as the starting value of the accumulation.

3. The Accumulation Function F(x)
Example
, find F(2), F(0), F(-3).

4. The Accumulation Function F(x)
Example
, find F(2), F(0), F(-3).
* The value of the accumulation function at the starting point a is zero.

5. The Accumulation Function F(x)
The accumulation function of a function f(t) is
How are F and f related??? f(t) is measured in dollars per day where t is # days after Jan. 1. What are the units on
g(t) is measured in miles per hour where t is the number of hours driving. What are the units on

6. The Accumulation Function F(x)
The accumulation function of a function f(t) is,
How are F and f related???
f is the rate of change of F
f(x) = F’(x)

7. Sketching Accumulation Graphs
The graph of a function f(t) is given below.
Sketch the following:
f(t) 4 2 -1 -2 -4
Tip: Sketch the graph first then shift it up or down if needed.

8. Sketching Accumulation Graphs
The graph of a function f(t) is given below.
Sketch the following:
f(t) -1