1. MAT 1236 Calculus III Section 15.3 Part II Double Integrals Over General Regions http://myhome.spu.edu/lauw

2. HW&… WebAssign 15.3 II (7 problems, 51 min.) Quiz: 15.1-15.3

3. Preview Change the order of integration Properties (relation to section 6.1)

4. Order of Integration If D is both type I & type II, then

5. Example 1 Evaluate

6. Example 1 The inner integral is impossible/difficult to evaluate Switch the order of integration

7. Example 1 Sketch and state the region of integration and change the order of integration

8. Example 1 Sketch and state the region of integration and change the order of integration Type I

9. Example 1 Sketch and state the region of integration and change the order of integration

10. Example 1 Sketch and state the region of integration and change the order of integration

11. Example 1

12. Summary Notice that the inner integral is difficult to evaluate Sketch the region Reverse the order of integration Evaluate the iterated integral

13. Expectations You are expected to label your graph Transitional integral You are expected to write down the two set descriptions of the domain D.

14. Properties and others….

15. Property

16. Consistency How do we know our calculus “system” is consistent? (No conflicts, agree with each other)

17. Consistency How do we know our calculus “system” is consistent? (No conflicts, agree with each other) Volume formula “implies” area formula via

18. Type I: Region Bounded Above/Below

19. Type II: Region Bounded Left/Right