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Centroid of Area Between Two Circles

MVCALC-G4YJDY

Find the centroid (center of mass) of the constant density region $R$ between two circles:

$$C_1=\{(x,y): (x-1)^2+y^2=1\}$$

...and:

$$C_2=\{(x,y): x^2+y^2=9\}$$

A

$(\cfrac{9}{8}-\cfrac{31}{12\pi}, 0)$

B

$(0, \cfrac{9}{8}-\cfrac{31}{12\pi})$

C

$(\cfrac{8}{9}-\cfrac{\pi}{3}, 0)$

D

$(0, \cfrac{8}{9}-\cfrac{\pi}{3})$

E

$(2,0)$