Day 50 in MAT229

Last time: Exam 3

Next time: Section 13.1

Today:

Announcements:
- Exam 3 returned
- Curve: add 20 points, and see me to discuss your exam and get 1/5 of the points you missed back (after the curve is applied).
Section 12.4: polar areas and arc lengths
- Let's convince ourselves of the derivation of the polar area formula:
  
  ${A=\frac{1}{2}\int_{\alpha}^{\beta}r^2d\theta}$
- And do some examples:
  - A relatively simple one: #4, p. 635.
  - A little more complicated: #16, p. 636.
  - Now you try: #13, p. 636.
- The arc length formula is also relatively easy: we get it by considering the polar representation as a parametric representation of the coordinates x and y:
  
  ${A=\int_{\alpha}^{\beta}\sqrt{f(\theta)^2+f'(\theta)^2}d\theta}$

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