1. SECTION 5.2 Area

2. Antiderivatives

3. Summation An Important Example:

4. Example 1

5. Example 2

6. Summation Formulas

7. Example 3

8. Area How does all of this relate to the concept of area? The sum of the areas of “regular” shapes can be used to estimate the area of “irregular” shapes.

9. A Famous Example Archimedes (287-212 B.C.) Use of the Method of Exhaustion Used the method to derive formulas for the areas of ellipses, parabolic segments, and sectors of a spiral. Considered to be the greatest applied mathematician in antiquity.

11. Our Use of the Method in Calculus

12. Example 4

13. Example 5 Bound the area of the shaded region by approximating the upper and lower limit sums. Use rectangles of length 1.

14. Example 6

15. Example 7

16. Example 8

17. The Area of a Region in the Plane

18. Example 9