This lesson introduces the definite integral as a convenient way of expressing the area under a curve. Students learn to recognize the parts of a definite integral. They also learn how to write a definite integral given a shaded area as well as given a function and an interval. Students learn to compare limits of Riemann sums with definite integrals and they also see how to evaluate a definite integral for simple areas using geometry.

This lesson is appropriate for both AP Calculus AB and BC.

Detailed answer keys are included.

The topics covered include:

-Definition of a Definite Integral

-Identifying Areas as Definite Integrals

-Writing Riemann Sums as Definite Integrals

-Net Area

-Using Geometry to Calculate Definite Integrals

-Properties of Definite Integrals

-Applying the Properties of Definite Integrals

-Definite Integrals of Odd and Even Functions

In this product, you will find the following:

-Powerpoint Presentation (31 slides)

-Guided Notes (4 pages, a "filled in" copy is also included)

-Do Now Slips (4 slips on one page, answers included)

-Exit Ticket Slips (4 slips on one page, answers included)

-Homework Assignment (2 pages, a detailed answer key is included)

This lesson is part of a larger unit on Integrals. The complete unit includes the following:

-Areas and Distances

-Estimating the Area Under a Curve

-Finding the Area Under a Curve

-Definite Integrals

-The Fundamental Theorem of Calculus

-Indefinite Integrals

-The Substitution Rule

-The Average Value of a Function

-The Accumulation Function

Save money and buy all nine lessons as a bundle:

-Integrals Unit Bundle