Investigates the second half of the Thm. Time is spent looking at examples as well as finding anti derivatives with specific conditions

The lesson begins with a connection being illustrated between position and velocity. This is a review. However, the area under the velocity graph is calculated and the connection back to position is explored. This lesson also examined a graph and a function defined as the integral of another function. The derivative of the integral is examined.

Exploring through Sketchpad, the connection between a function and a function representing the signed area from a to x is explored. The function [F(x)] that is the signed area from a to x for the function f(x) is revealed to be the anti-derivative.

Exploring through Sketchpad, the connection between a function and a function representing the signed area from a to x is explored. The function [F(x)] that is the signed area from a to x for the function f(x) is revealed to be the anti-derivative.

Rules for the definite integral are explored.

A reimann sum is constructed and then developed into the definite integral. A connection to area is explored. Definite integrals are evaluated using knowledge of geometry.

Explore how the area under a curve can connect to a real life situation involving velocity and time. Rectangle methods are explored to approximate the area.

Examine a more complicated related rate question

Examine two related rate questions

Using Differentials to approximate changes in the function