Find length of curve. Integral of sec?

[phantomcow2]

Homework Statement

Find the length of the curve y=ln(cosx) from 0 to pi/3

Homework Equations

integral of (1+(y')^2)^1/2

The Attempt at a Solution

First, find y'. y' is equal to -sin/cos, or simply -tan(x).

$$\int$$$$\sqrt{1+(-tan(x)^{2}}$$
= $$\int$$$$\sqrt{sec(x}$$

Homework Statement

Can this possibly be right so far? This is a horrendous integral. I've expended so much energy on this problem, but if someone can at least validate that I am on the right track, I'll post my work from here out.

 

[rock.freak667]

$$\int$$$$\sqrt{1+(-tan(x)^{2}}$$
= $$\int$$$$\sqrt{sec(x}$$

$$1+tan^2x=sec^2x \Rightarrow \sqrt{1+tan^2x}= \sqrt{sec^2x}=secx$$

 

[phantomcow2]

Thank you so much.