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Math Help - Can somebody explain why you take the derivative of a curve to find its length?

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    Question Can somebody explain why you take the derivative of a curve to find its length?

    Given a curve:

    G(t)=\binom{t}{y(t)}

    It goes between the two points:

    A=(t_1,y_1) B=(t_2,y_2)

    To find its length:

    Length=\int_{t_1}^{t_2}\sqrt{\left(\frac{d}{dt}G(t  )\right)^2}\, dt

    What I understand is that you use the integral going from the values t_1 and t_2 to find the entire length between these two values. The squareroot and the exponential comes from the Pythagorean theorem to find the hypotenuse.

    What I don't understand is why we take the derivative of the curve G(t).
    Last edited by MathIsOhSoHard; April 15th 2012 at 04:18 AM.
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  2. #2
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    Re: Can somebody explain why you take the derivative of a curve to find its length?

    Arc length - Wikipedia, the free encyclopedia

    Go to "Finding arc lengths by integrating".
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