Area under a rate function equals net change

The  exercise appears under the Integral calculus Math Mission. This exercise uses the rate function, or derivative, and connects it to an amount of change.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the total change: This problem presents a graph that is said to represent a rate of change. The student is asked to find the amount of net change that occurs in the situation by using the graph.Auarfenc1.png

Strategies
Knowledge of geometric area formulas and the concept of integration as area under the curve are encouraged to ensure success on this exercise.
 * 1) The amount of net change is the area under the curve, or integral.
 * 2) To increase efficiency, cut the diagram into several rectangles and triangles and find the area of each separately.
 * 3) Graph that is below the x-axis should be treated as negative area.

Real-life Applications

 * 1) Geometrically an integral can be used to find area and volume formulas.
 * 2) Several of the problems in this exercise are applications.
 * 3) This exercises illustrates how information from the entry at places like Disneyland can be used to assess how many people are in the park at a given time.
 * 4) These techniques can be used to understand traffic patterns in cities.