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Antiderivatives

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.

DEFINITION

Suppose

- What is its antiderivative?

We can make some guesses

They all fit!

Theorem

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!

This is read The antiderivative of f with

respect to x or the indefinite integral of f with

respect to x is equal to..

What is the Antiderivative of

Derivative

We kinda multiply

Take the integral of both sides

Some General Rules

They are just the derivative rules in reverse

Differentiation Formula

Integration Formula

Pulling out a konstant

Some General Rules

Differentiation Formula

Integration Formula

Sum / Difference Rule for Integrals

Power Rule for Integrals

Some General Rules

Differentiation Formula

Integration Formula

All the other trig functions follow

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