(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ok, the problem is there are two curves and I need to find out which is shorter. I can't find the first one so I'll just post that. The other should be easy after I learn how to get this one.

2. Relevant equations

The first curve is:

3. The attempt at a solution

I used the formula and worked it down to .

I've also seen some similar problems to this where people recommended trig substitutions. I tried substituting tan u in which gave me sec^2 u under the radical. If I go that route, I don't know the integral of sec or how you could carry on. The other way I thought you could do this was to just simplify (from the last picture I posted) and try to integrate that... but that would be rough. Any tips?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Using integral to find length of curve

**Physics Forums | Science Articles, Homework Help, Discussion**