1. 1 Definite Integrals Section 4.3

2. 2 The Definite Integral The definite integral as the area of a region: If f is continuous and non-negative on the closed interval [a, b], then the area of the region bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b is given by Area = This is called the definite integral. f ab A

3. 3 The Definite Integral where c i is any point in the ith interval and ******************************************** At this point, we evaluate a definite integral using area formulas of common geometric regions, if possible. (In the next section, we will calculate the definite integral using other methods)

4. 4 Using Common Geometric Figures Example:

5. 5 Using Common Geometric Figures Example:

6. 6 Using Common Geometric Figures Example:

7. 7 Using Common Geometric Figures Example:

8. 8 Properties of the Definite Integral by definition a b f c

9. 9 Definite Integrals ab f A1A1 A2A2 A3A3 = area above – area below

10. 10 Properties…

11. 11 Example Ifand then find

12. 12 Example Set up a definite integral that yields the area of the region.

13. 13 Example Set up a definite integral that yields the area of the region.

14. 14 Homework Section 4.3 page 278 # 13 – 19 odd, 23 – 43 odd