1. Antiderivatives

2. Mr. Baird knows the velocity of particle and wants to know its position at a given time Ms. Bertsos knows the rate a population of bacteria is increasing and she wants to know what the size of the population will be at a future time. In each case the rate of change (the derivative) is known….but what is the original function? The original function is called the ANTIDERIVATIVE ANTIDERIVATIVE of the rate of change.

3. A function is called an antiderivative of on an interval if for all x in. DEFINITION

4. Suppose What is its antiderivative? We can make some guesses They all fit!

5. Theorem If is an antiderivative of on an interval, then the most general antiderivative of on is where is an arbitrary constant.

6. Finding an antiderivative is also known as Indefinite Integration and the Antiderivative is the Indefinite Integral (Especially for us old guys!) And the symbol for integration is an elongated S More on why it’s an S later!

7. Integrand Variable of Integration Constant of Integration This is read: The antiderivative of f with respect to x or the indefinite integral of f with respect to x is equal to…..

8. What is the Antiderivative of Derivative We “kinda” multiply Take the integral of both sides We know what to differentiate to get

9. Some General Rules They are just the derivative rules in reverse Differentiation Formula Integration Formula “Pulling out a konstant”

10. Some General Rules Differentiation Formula Integration Formula Sum / Difference Rule for Integrals Power Rule for Integrals

11. Some General Rules Differentiation Formula Integration Formula All the other trig functions follow