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Thread: Quick arc length question

  1. #1
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    Quick arc length question

    Hi all, i wonder if anyone can help me with this question, tried and failed&im wasting too much time on this one!

    Determine the arc lenth of:
    $\displaystyle
    \begin{gathered}
    y = \ln \cos ecx \hfill \\
    x = \frac{\pi }
    {4} \hfill \\
    x = \frac{\pi }
    {3} \hfill \\
    \end{gathered}
    $
    between those limits
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  2. #2
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    Quote Originally Posted by MexicanGringo View Post
    Hi all, i wonder if anyone can help me with this question, tried and failed&im wasting too much time on this one!

    Determine the arc lenth of:
    $\displaystyle
    \begin{gathered}
    y = \ln \cos ecx \hfill \\
    x = \frac{\pi }
    {4} \hfill \\
    x = \frac{\pi }
    {3} \hfill \\
    \end{gathered}
    $
    between those limits
    $\displaystyle \frac{dy}{dx} = -\cot x$.

    $\displaystyle \sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \frac{1}{\sin x}$.

    Substitute into the arc length formula and integrate.
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