Day 19 in Mat122

Today:

• Return exam 1:
  • Exam 1
  • key
  • Curve: 10*x/7+10 (linear transformation)
  • You can get 20% of your lost points by meeting with me to go over your exam.

• Hand in Section 6.2 homework

• 6.3 homework will be due Friday

• Directed reading handout: Section 6.4 (html) (pdf)

• 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