1. Antiderivatives

2. Antiderivatives The original function is called the
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 of the rate of change.

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

4. What is its antiderivative?
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. Constant of Integration
Integrand
Constant of Integration
Variable 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
We “kinda” multiply
Take the integral of
both sides
We know what to differentiate
to get

9. They are just the derivative rules in reverse
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

12. Basic Integration Formulas