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Math Help - A straightforward question (but help needed!)

  1. #1
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    A straightforward question (but help needed!)

    Recall how to calculate the arc-length and the curvature of a parametric curve \delta:\ I\rightarrow $\mathbb{R^2}

    Any help as to the steps involved greatly appreciated (running low on time before the exam day after tomorrow).
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: A straightforward question (but help needed!)

    If the curvature is expressed in the form y=f(x)\ ,\ a<x<b, then the arc lenght is ...

    L= \int_{a}^{b} \sqrt{1+ (y^{'})^{2}}\ dx (1)

    Kind regards

    \chi \sigma
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  3. #3
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    Re: A straightforward question (but help needed!)

    Thanks.
    I don't quite follow the 'y = f(x)'. i thought parametric curves looked like eg x = 2t +3, y = t^2 +2 e.t.c...
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  4. #4
    MHF Contributor chisigma's Avatar
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    Re: A straightforward question (but help needed!)

    If the curve is defined in parametric form x=x(t)\ ,\ y=y(t)\ ,\ a<t<b , then ...

    L=\int_{a}^{b} \sqrt {[x^{'}(t)]^{2} + [y^{'}(t)]^{2}}\ dt (1)

    Kind regards

    \chi \sigma
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  5. #5
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    Re: A straightforward question (but help needed!)

    I'm sure now that's the formula i was looking for. Thanks A lot.
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