Originally Posted by

**Hellreaver**

Find the length of the following parametric curve $\displaystyle \color{red}x$ $\displaystyle = a(\cos t + \ln \tan(t/2)), \ \ y= a \sin t,$ from the point (0,a) to the point (x,y).

I need to use the formula

$\displaystyle L= \int \sqrt{( \frac {dx}{dt}^2)+ (\frac {dy}{dt}^2)}dt$

but I'm not sure what the limits of integration are so I can evaluate the result.

As well, would $\displaystyle \frac {dx}{dt}$ be $\displaystyle a(-sin t+ \frac {1}{tan \frac {t}2})$? Or am I differentiating the ln incorrectly?