# Thread: Surface area of a cycloid

1. ## Surface area of a cycloid

Hi all...working on coming up with the surface area of a cycloid. I'll spare you the process of getting there, but what I've come up with is this integral:

The a is a positive constant defined in the original question.

I don't know how to solve that integral, though. I've played around with some identities in hopes of finding one that would help but I haven't come up with anything. What's the solution to this one?

2. Originally Posted by Malaclypse
Hi all...working on coming up with the surface area of a cycloid. I'll spare you the process of getting there, but what I've come up with is this integral:

The a is a positive constant defined in the original question.

I don't know how to solve that integral, though. I've played around with some identities in hopes of finding one that would help but I haven't come up with anything. What's the solution to this one?
Hint $1-cost=2sin^2(\frac{t}{2})$

3. That pretty much did the trick, thank you!!!

I still have one problem, though...when I work that through I end up with:

Edit: Duhhh...nevermind. It's been a long night. It helps when you actually put your original variable back in after u-sub...