Exercises of aplication of Green's theorem

Question

Use Green's Theorem to find the limited area above the $x$-axis and below the circle of centers $C_1(0,1)$ and $C_2(2,1)$, both of radio equal to $1$.

$C_1: x^2+(y-1)^2=1$ and $C_2: (x-2)^2+(y-1)^2=1$

I am a bit confused on how to use this theorem the proposed problem, can you help me?

Answer 1

See Calculus Vol.2 Tom Apostol page 383.

Answer 2

Use Green's theorem to the field $\vec{F}=\langle -y,x \rangle$. Parametrise the Boundary curve.