(Solved): (a) (I pt) Compute the ares of the region \[ R_{1}=\left\{(x, y): 1 \leq x^{2}+y^{2} \leq 4, x \leq ...

(a) (I pt) Compute the ares of the region \[ R_{1}=\left\{(x, y): 1 \leq x^{2}+y^{2} \leq 4, x \leq 0\right\} \] using Polar coordinates. (b) (1 pt) Demonstrate the symametry property \[ 2 \iint_{F_{4}} d A=\iint_{R_{2}} d A \] where \( R_{2}=\left\{(x, y): 1 \leq x^{2}+y^{2} \leq 4\right\} \). le. Compute both quantities and show they are the same. (For the region \( R_{2} \), notioe that there are no restrictions on \( x \) values)