Dr Thompson's AP Calculus University High School

Integration by parts. Tabular integration and a problem involving an unknown integral is investigated.

Using integration by parts. Investigate problems using this specific method.

2 examples of using a method of u substitution for indefinite integrals.

An introduction to first order differential equations and slope fields. A slope field is graphed using a TI 89. Connections to the fundamental theorem of calculus are made.

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.

Rules for the definite integral are explored. Average value of a function.

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.