# Integrating to find the length of a Cardiot Curve

1. Nov 28, 2009

### Jim4592

1. The problem statement, all variables and given/known data
find the length of the cardiot r = 1+cos(Θ)

I'm going to use { as the integral sign
all integrals are definite between 0 and Pi

2. Relevant equations
L = 2 {sqrt[(r^2(Θ))+(dr/dΘ)^2]dΘ

3. The attempt at a solution
L=2* {sqrt[2+2cos(Θ)] dΘ

I'm having a really hard time trying to integrate sqrt[2+2cos(Θ)] dΘ and was hoping someone could explain to me how you integrate that.

Thanks.

2. Nov 28, 2009

### xeno_gear

Personally, I would start by doing

$$\int_0^\pi \sqrt{2 + 2\cos\theta} \, d\theta = \sqrt{2}\int_0^\pi \sqrt{1 + \cos\theta}\, d\theta.$$

It's totally not necessary, but it sort of simplifies things. Then you want to use the identity
$$\frac{1 + \cos\theta}{2} = \cos^2\frac{\theta}{2}$$

Multiply both sides of that identity by 2, then you'll have something a little nicer to work with..