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Golden Spike National Historic Site, Promontory, Utah Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999 7.4 Day 1 Lengths of Curves

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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. Length of Curve (Cartesian)Lengths of Curves:

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Example: Now what? This doesn’t fit any formula, and we started with a pretty simple example! The TI-89 gets:

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

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Example: You may want to let the calculator find the derivative too: Important: You must delete the variable y when you are done! ENTER F44 Y STO Y

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Example:

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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. ENTER X STO

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Don’t forget to clear the x and y variables when you are done! ENTER F44 Y X

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10.1 Parametric functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008 Mark Twain’s Boyhood Home Hannibal, Missouri.

10.1 Parametric functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008 Mark Twain’s Boyhood Home Hannibal, Missouri.

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