1. Chapter 5 – The Definite Integral

2. 5.1 Estimating with Finite Sums Example Finding Distance Traveled when Velocity Varies

4. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x=0 to x=3

5. p.270 (1-19, 26, 27)

6. 5.2 Definite Integrals Sigma notation enables us to express a large sum in compact form: Ex)

7. The Definite Integral as a Limit of Riemann Sums

8. We have that Upper limit Integral sign Lower limit Integrand Variable of Integration

9. Example Using the Notation Area Under a Curve

10. Notes about Area The Integral of a Constant

11. Evaluate the following integrals:

12. p.282 (1-27, 33-39) odd

13. 5.3 Definite Integrals and Antiderivatives

15. Ex: Show that the value of Average (Mean) Value

16. The Mean Value Theorem for Definite Integrals

17. Integral Formulas This is known as the indefinite integral. C is a constant.

18. Evaluate:

19. p. 290 (1 – 29) odd 19 – 29 note Do (31-35) After 5.4

20. 5.4 Fundamental Theorem of Calculus The Fundamental Theorem of Calculus – Part 1

21. Evaluate the following: Find

22. Find a function y = f(x) with derivative That satisfies the condition f(3) = 5.

23. The Fundamental Theorem of Calculus, Part 2

24. How to Find Total Area Analytically Find the area of the region between the curve y = 4 – x 2, [0, 3] and the x-axis. Look at page 301 example 8.

25. p.302 (1-57) odd

26. 5.5 Trapezoidal Rule

27. The Trapezoidal Rule

28. Use the trapezoidal rule with n = 4 to estimate. Compare with fnint. Ex: An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. What was the average temperature for the 12-hour period? TimeN1234567891011M Temp63656668706968 6564625855

29. Simpson’s Rule Ex: Use Simpson’s rule with n = 4 to approximate

30. p.312 (1-18)