# Homework Help: Find length of curve. Integral of sec?

1. Jun 18, 2009

### phantomcow2

1. The problem statement, all variables and given/known data
Find the length of the curve y=ln(cosx) from 0 to pi/3

2. Relevant equations
integral of (1+(y')^2)^1/2

3. The attempt at a solution
First, find y'. y' is equal to -sin/cos, or simply -tan(x).

$$\int$$$$\sqrt{1+(-tan(x)^{2}}$$
= $$\int$$$$\sqrt{sec(x}$$
1. The problem statement, all variables and given/known data

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.

2. Jun 18, 2009

### rock.freak667

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

3. Jun 18, 2009

### phantomcow2

Thank you so much.