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Antiderivatives

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.

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Antiderivatives

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

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

  5. If is an antiderivative of on an interval , then the most general antiderivative of on is whereis an arbitrary constant. 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 it’s an S later!

  7. Constant of Integration Integrand 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. We know what to differentiate to get 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

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