1. MAT 1235 Calculus II Section 5.3 Volumes by Cylindrical Shells http://myhome.spu.edu/lauw

2. Homework WebAssign HW 5.3 It is crucial to have a correct (mental) images.

3. Tomorrow Section 6.1 Inverse Functions Review your algebra/pre-calculus… What is an inverse function? What is a one-to-one function? Also, we will talk about possible scheduling changes next week.

4. Preview 5.2 Find volumes by the “Disc” method 5.3 Find volumes by the “Shell” method Can handle cases where the Disc method does not work well.

5. Recall Any limit of the form : can be interpreted as

6. Example 1 (Disc Method)

10. Cylindrical Shells

12. use midpoint as the sample point

13. Cylindrical Shells use midpoint as the sample point

14. Cylindrical Shells

17. Shell Height Radius of the Shell

18. Example 1 (Shell Method) Find the volume of the solid obtained by rotating about the y-axis the region bounded by and

19. Example 1

21. Example 2 Find the volume of the solid obtained by rotating about the y-axis the region bounded by and

22. Example 2

25. Remark:

26. Example 3

29. Remark:

30. Example 4