# Math Help - Quick arc length question

1. ## 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:
$
\begin{gathered}
y = \ln \cos ecx \hfill \\
x = \frac{\pi }
{4} \hfill \\
x = \frac{\pi }
{3} \hfill \\
\end{gathered}
$

between those limits

2. Originally Posted by MexicanGringo
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:
$
\begin{gathered}
y = \ln \cos ecx \hfill \\
x = \frac{\pi }
{4} \hfill \\
x = \frac{\pi }
{3} \hfill \\
\end{gathered}
$

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.