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7.4

Lengths of Curves. 7.4. Length of Curve (Cartesian). Lengths of Curves:. If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem:. We need to get dx out from under the radical.

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7.4

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  1. Lengths of Curves 7.4

  2. Length of Curve (Cartesian) Lengths of Curves: If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical.

  3. Now what? This doesn’t fit any formula, and we started with a pretty simple example! Use your calculator to integrate Example:

  4. If we check the length of a straight line: Example: The curve should be a little longer than the straight line, so our answer seems reasonable.

  5. Example:

  6. If you have an equation that is easier to solve for x than for y, the length of the curve can be found the same way. Notice that x and y are reversed.

  7. Homework Page 399 #1-11 odd, 12,17,18,24

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