Find Area with Theorem of Green - center - radius

1. Nov 25, 2015

masterchiefo

1. The problem statement, all variables and given/known data
x(t) = 6cos(t)−cos(6t) y(t) = 6sin(t)−sin(6t) 0 <= t <= 2*pi
I need to find the area cm2 with Th Green.

I need to find the radius and the center coordinate

2. Relevant equations

3. The attempt at a solution
$= integral 1/2* ( 2*pi$0 ((x)dy - (y)dx) dt )

1/2 (2*pi\$0 ((6cos(t)−cos(6t)*6cos(t)−6cos(6t) - (6sin(t)−sin(6t)*6sin(t)−6*sin(6t)) dt)

= 42*pi

How do I find the center? is it (0,0)?

2. Nov 25, 2015

RUber

The center should be (0,0). This can be shown rather clearly by saying that
$x_1(t)=6 \cos (t)\quad y_1(t) =6\sin(t)$ is a circle centered at (0,0),
and so is $x_2(t)=\cos (6t)\quad y_2(t) =\sin(6t)$.

$\text{Area} = \frac12 \int_0^{2\pi} \left( 6 \cos (t)-\cos (6t) \right) \left( 6 \cos (t)-6\cos (6t) \right) - \left( 6\sin(t)-\sin(6t) \right) \left( - 6\sin(t) + 6\sin(6t) \right) \, dt$