1. Antiderivatives and Indefinite Integrals Modified by Mrs. King from Paul's Online Math Tutorials and Notes http://tutorial.math.lamar.edu/AllBrowsers/2413/ IndefiniteIntegrals.asp

2. Introduction In the past two chapters we’ve been given a function f(x) and asking what was the derivative of this function. We now want to turn things around and ask what function we differentiated to get the function f(x).

3. Example 1 What function did we differentiate to get the following function:

13. Process for finding an Antiderivative: This is the reverse of differentiation, so we are going to add one to the exponent and then divide by that new exponent.

14. Constants We know that the derivative of a constant is zero and any function of the form will result in the function f(x) upon differentiating.

15. Definitions Given a function f(x) an anti-derivative of f(x) is any function F(x) such that

16. Definitions If F(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted

17. Definitions In this definition the ∫ is called the integral symbol, f(x) is called the integrand, x is called the integration variable and the “c” is called the constant of integration.

18. Example #2

20. Example #3

22. Example #4

25. Example #5

28. Example #6

30. Example #7