Integrating to find the length of a Cardiot Curve

[Jim4592]

Homework Statement

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

Homework Equations

L = 2 {sqrt[(r^2(Θ))+(dr/dΘ)^2]dΘ

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.

 

[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..