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8.1 Arc Length

8.1 Arc Length. We can think of the length of an arc as the limit of the sum of segment lengths a s the number of segments approaches infinity:. E ach segment has length Then, by the Mean Value Theorem, there’s a number on Such that . Then.

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8.1 Arc Length

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  1. 8.1 Arc Length

  2. We can think of the length of an arc as the limit of the sum of segment lengths as the number of segments approaches infinity:

  3. Each segment has length Then, by the Mean Value Theorem, there’s a number on Such that

  4. Then

  5. Then our arc length L is Of course this is:

  6. If the curve has equation x = g(y), and g’(y) is continuous, the arc length is

  7. Example: find the length of the curve between the points (1,1) and (4,8):

  8. Example: find the length of the curve for

  9. Homework p. 552 # 3, 5, 7, 9, 11

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