you say this in your original post ...
then you say this in a subsequent post ...I am stuck and I dont know how to integrate sqrt(sec^2).
pardon me if I do not understand your difficulty.I know what the integral of sqrt(sec^2) is. But I know dont know how I will solve it comes to Exams.
here is the arclength calculation ...
$\displaystyle
\int_0^{\frac{\pi}{3}} \sec{x} \, dx
$
$\displaystyle \left[\ln(\sec{x} + \tan{x})\right]_0^{\frac{\pi}{3}}$
$\displaystyle
\left[\ln\left(\sec{\frac{\pi}{3}} + \tan{\frac{\pi}{3}}\right)\right] - \left[\ln\left(\sec{0} + \tan{0}\right)\right]
$
$\displaystyle
\left[\ln\left(2 + \sqrt{3}\right)\right] - \left[\ln\left(1+0\right)\right]
$
$\displaystyle
\ln(2 + \sqrt{3})
$