1. MAT 1226 Calculus II Section 10.4 Areas and Length in Polar Coordinates http://myhome.spu.edu/lauw

2. Classroom swap this week... Wednesday – no class if we finish everything today RF – switch to OMH 245

3. HW… WebAssign 10.4 (17 problems, 151 min.) Do your HW ASAP. Do not wait until Wednesday or Thursday to do your HW. Quiz 02: 10.3, 10.4 –Make sure you understand how to do all the problems, not just the easy one

4. Preview Area: Regions defined by polar equations is different from the regions defined by rectangular equations Derive the formula Examples Arc Length (from section 10.2)

5. Common Assumptions It is a custom to assume the obvious geometric symmetries in regions defined by polar equations

6. To Save Time… We are going to focus on setting up the integral. We will not actually do all computations.

7. Recall: Riemann Sum i th subinterval sample point

8. Recall: Riemann Sum

9. Area

13. Example 1 Find the area enclosed by one loop of

14. Example 1

16. Example 2 Find the area of the region that lies inside and outside

17. Example 2

19. Arc Length

20. Arc Length 1st Formula (10.2, 2 derivatives)

21. Arc Length 2nd Formula (1 derivative)

22. Example 3 Find the length of