Antiderivatives

1
Antiderivatives
2
Antiderivatives

• 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
4
Suppose

• What is its antiderivative?

We can make some guesses
They all fit!
5
Theorem
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 its an S later!
7
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
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