4. (20 pts) Let R be a ring of radius 2 centered at (1,1) and pt,…

4. (20 pts) Let R be a ring of radius 2 centered at (1,1) and pt, y) = x2 + y2 – 2.– 2y + 2 be a density function. (a) (2 pts) Which equation calculates the total mass? i pardy ii. pds ii. S xpdr + [ updy iv. Izpds + / upas (b) (4 pts) Amy intended to find the total mass. She noticed that the polar coordinates might be suitable, so she set x = 2 cost, y = 2 sint and substitute p as p2 – 2r cost – 2r sint +2. Then she formulated the integral as M = [ (6 – 4 cost – 4 sint). 2 dt. (Hint: What is the para- However she made a mistake. Pleas help her find the mistake. metric curve C in her formulation?) (c) (6 pts) Find the right formulation and calculate the total mass M. (d) (8 pts) Prove that the center of mass is (1,1).