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Math Help - 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:
    <br />
\begin{gathered}<br />
  y = \ln \cos ecx \hfill \\<br />
  x = \frac{\pi }<br />
{4} \hfill \\<br />
  x = \frac{\pi }<br />
{3} \hfill \\ <br />
\end{gathered} <br />
    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:
    <br />
\begin{gathered}<br />
y = \ln \cos ecx \hfill \\<br />
x = \frac{\pi }<br />
{4} \hfill \\<br />
x = \frac{\pi }<br />
{3} \hfill \\ <br />
\end{gathered} <br />
    between those limits
    \frac{dy}{dx} = -\cot x.

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

    Substitute into the arc length formula and integrate.
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