4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

4.1 Antiderivatives and Indefinite Integration Learning Targets 1. Write the general solution of a differential equation 2. Use indefinite integral notation for antiderivatives 3. Use basic integration rules to find antiderivatives 4. Find a particular solution of a differential equation 5. Plot a slope field 6. Working backwards in physics

Intro/Warm­up 1 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

Note: I am changing up the procedure of the class! When you walk in the class, you will put a tally mark on those problems that you would like me to go over, and you will turn in your homework with your name, the section and the page of the assignment.

Order of the day 2 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

Vocabulary First, find a function F whose derivative is .

because any other function F work?

So represents the family of all antiderivatives of . The constant C is called the constant of integration. The family of functions represented by F is the general antiderivative of f, and is the general solution to the differential equation

The operation of finding all solutions to the differential equation is called antidifferentiation (or indefinite integration) and is denoted by an integral sign:

is read as the antiderivative of f with respect to x.

Vocabulary 3 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

Nov 28­9:38 AM 4 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

∫ Use basic integration rules to find antiderivatives The Power Rule: where

1. Solve the differential equation

So the solution to is

2. Evaluate (see tables on next slide)

3. Evaluate (see tables on next slide)

I.Use basic integration rules to find antiderivatives 5 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

Basic Integration Rules 6 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

∫∫Initial Conditions and Particular Solutions 4. For the differential equation find the general equation. If the initial condition is find the particular solution.

II. Initial Conditions and Particular Solutions 7 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

∫∫∫ Slope Fields 5. Draw a slope field for

III. Slope Fields 8 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

To find a program on Slope Fields:

Slope field programs 9 4.1 AP Calc Antiderivatives and Indefinite Integration.notebook November 28, 2016

Your Homework AB Calculus 4.1 p.255 #2,3,6,15‐39(x3),45‐66(x3), 67,68,71,81,87* *=use calcchat.com

BC Calculus 10.5 p.747 #12,24,30,39,44,47,57,67,73‐77

Homework 10