Published on December 03, 2011

#### Objectives

- Given a graph of a function, determine over what intervals the definite integral of that function will be positive, negative, or zero
- Make generalizations about the behavior of the definite integral of any continuous function.
- Explain the mathematical deficiency in the "area under the curve" description of the definite integral.

#### Vocabulary

- Signed area
- Definite integral
- Continuous function

#### About the Lesson

The intent of this lesson is to help students make visual connections between the definite integral of a function and the signed area between the function and the x-axis. In particular, this lesson provides opportunities to develop a mathematically accurate conception of the definite integral that avoids the "area under the curve" description of the definite integral.