The Indefinite Integral

1. The Indefinite Integral

2. You will be going through this power point and learning how to solve the most basic indefinite integral. • After reading each slide there will be buttons at the bottom of that slide, you will use the buttons to navigate through the power point. You can go forward and backwards. When it is time for the quiz there will be a button that will take you to the quiz.

3. What this has to do with you? • The indefinite integral will be used a lot more in the later chapters, you need to know this in order to pass this class. • You will also need this in Calculus II and in many engineering classes. • Ultimately, you will need this to graduate.

4. The Indefinite Integral • The indefinite integral that you will learn how to solve involves the simplest function, the polynomial. • At this point in the course you will only learn how to solve polynomial functions, we will get into more complex functions later in the course.

5. The Indefinite Integral • This symbol tells you that you need to take the integral of the following function. • EX: ∫ 5x3+ x2 -10 dx

6. Integral Compared to the Derivative • The integral is the complete opposite of the derivative when the function is a polynomial. • When taking the derivative of a polynomial you use the power rule; with the integral being the opposite, you will be using the power rule in reverse. Note: All the problems, right now are dealing with polynomials!

7. Example of taking the DERIVATIVE EX: f(x)= 5x2+x-4 f´(x)= 10x+1 Note: When finding the derivative you multiply the coefficient with the power, of that same term, and subtract the power by one. Now we will find the Integral by using the opposite of the Power Rule.

8. Integral • So after using the Power Rule to find the derivative we will do the opposite to find the integral. • Now we will add one to the power, and divide the coefficient with the new power, of that same term. Ex: ∫6x2+2x-1 dx = 2x3+x2-x

9. Integral Cont. WAIT!!! We are still not done. • When taking the integral you will always have a +C at the end. ( C standing for constant) • Can you guess as to why that might be?

10. When taking the derivative we see that we lose a constant in the process. • When we take the integral of a function we have to put that constant back. The constant could have been anything so that is why we put a +C instead of some random number.

11. Example Going back to our first example we now see that, Ex: ∫6x2+2x-1 dx = 2x3+x2-x+C • These are the kind of problems that you will be doing on the quiz.

12. What you should know? • After going through this power point you should be able to find the Integral of a basic polynomial. • Now you will be quizzed on what you know.

13. Quiz Time!!! After starting the quiz you cannot go back through the power point. Good Luck! Quiz

14. Problem # 1 #1. ∫ xdx • A. 1 • B. 1/2xˆ2 +C • C. 5x+C A. 1 B. 1/2x2+C C. 5x+C

15. Problem # 2 ∫ 3x2+2 dx • A. xˆ3+2x+C • B. 3xˆ2+2+C • C. 6x A. x3+2x+C B. 3x2+2 C. 6x

16. Problem # 3 ∫ 20x4-3x2dx • A. 80xˆ3-4x • B. 4xˆ5-xˆ3 • C. 4xˆ5-xˆ3+C A. 80x5+6x3 B. 20x5-3x3+C C. 4x5-x3+C

17. Problem # 4 • ∫ 100x99dx • A. xˆ100+C • B. 100xˆ100+C • C. 100xˆ99+C A. x100+C B. 100x100+C C. 100x99+C

18. Problem # 5 • The Integral of ƒ´(x) is ƒ(x). • True • False True False

19. Incorrect Back

20. Correct Next Problem

21. Correct Next Problem

22. Correct Next Problem

23. Correct Next Problem

24. Correct Continue

25. You did great!!! • You have completed the quiz and this concludes the power point. You are now prepared to take the integral of a polynomial.

26. Reference • Indiana Standards and Resources. IN.gov. 14 April 2011. http://dc.doe.in.gov/Standards/AcademicStandards/ StandardSearch.aspx • Integral Symbol. Google Images. 14 April 2011. http:// www.google.com/images • International Society for Technology in Education. Iste. 12 April 2011. http://www.iste.org/standards/nets-for- teachers.aspx