Day 20 in Mat122

Today:

• 6.3 homework will be due Friday

• Section 6.3: Volumes of revolution
  • The definition:

    

    More generally...

  • We may want to consider two functions simultaneously, to give a "hollow" volume of revolution:

    

  • We can rotate about an axis other than the x-axis (e.g. the y-axis!), or even
    • the line x=-2, or
    • the line y=12 or y=15

  • Examples:
    • #2, p. 325
    • #15, p. 325
    • #32, p. 326
    • #38, p. 326
    • #40, p. 326

• Section 6.4:
  • The definition of "cylindrical shells":

    

    Which we refine....

  • Examples:
    • #7, p. 332
    • #16, p. 332 (use Newton's method)
    • #33-38, p. 333