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Math Help - Length of a curve

  1. #1
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    Length of a curve

    I am using this formula: sqrt((f'(x))^2+((g'(x)^2)) dx...Is that right? Because I keep getting weird answers that are too big! HELP!!!!


    Find the length of the curve defined by


    from to .
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  2. #2
    MHF Contributor
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    What formula is that? It's a single function of a single variable. Where did you get two functions?

    Let's see

    f(x)\;=\;4*x^{3/2}\;+\;3

    f'(x)\;=\;6*x^{1/2}

    \int_{5}^{8}\left(\sqrt{1\;+\;(6*x^{1/2})^{2}}\right)\;dx. You should be able to do that.

    I get \frac{1}{54}*(4913\;-\;181\sqrt{181})\;\approx\;45.887

    A quick look at the graph shows f(x) isn't far from straight on [5,8], so a rough estimate shows \sqrt{44^{2}+3^{2}}=44.10. I believe it.
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