AP Calculus 4.1 AntiDerivatives

AP Calculus 4.1 AntiDerivatives

Author: Danny Whittaker

This lesson will introduce the concept of the antiderivative.  After watching the four videos you will be able to:

  • Use indefinite integral notation for antiderivatives
  • Use basic integration rules to find antiderivatives
  • Understand the idea of a slope field
  • Write the general solution of a differential equation
  • Find a particular solution of a differential equation

Antidifferentiation is the inverse operation of differentiation.  It is used for many different things.  A main use is for solving differential equations to calculate the function.

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Introduction to the Antiderivative

Welcome to the new unit on antiderivatives.  You will want to print the PDF document so that you can have the notes in front of you as you watch the videos and can work through the examples with me.  In general as you do these you are responsible to know the content in the videos.  If you are able to complete the tutorial document and the quick quiz without watching all the videos, that is fine.  But please watch at least one of the videos so that you can properly comment in the quiz.

Review Notes

Here is a document to be looking at as you watch the video. I recommend printing and following along as you watch.

Full Screen

Source: Created by Tony Record of Avon High School in Indianapolis

Basics of Antiderivatives

First introduction to the idea of antidifferentiation with a few examples.

Integrating Trig Functions

Quick discussion of the basic trig integration rules along with two examples.

Antiderivatives and Slope Fields

A brief introduction to slope fields and differential equations.

Differential Equations

Two more examples solving differential equations.

Quick Quiz

Let me know what you've learned!