# Cardoid area

1. Feb 14, 2007

### rcmango

1. The problem statement, all variables and given/known data

Find the area of the region that is inside the circle r = 6cos(theta) but outside the cardoid r = 2 + 2cos(theta)

2. Relevant equations

r = 6·cosθ
r = 2 + 2·cosθ

3. The attempt at a solution

intersections of the two curves.

6·cosθ = 2 + 2·cosθ → 4·cosθ = 2

cosθ = 1/2 → θ = ±π/3

Can someone finish the integral for me, i'm not good at integrals, this is as far as i can get. thanks for any help.

A = 2 x (1/2) ∫ [(6·cosθ)² - (2 + 2·cosθ)²] dθ

2. Feb 14, 2007

### dextercioby

You still need a picture. Use math software and ask it to draw both graphs in polar coordinates (they should be $\left(\rho,\varphi\right)$, not "r" and "theta") and just then you can set up a correct integral.

3. Feb 15, 2007

### rcmango

No, I will not do the integral for you. I will give you a hint: to integrate $cos^2(\theta)$, use the trig identity [itex]cos^2(\theta)= \frac{1}{2}(cos(2\theta)+ 1).