Mass of lamina double integral

Question

Consider a lamina the shape of a region in the first quadrant, inside the circle (x − 2)²+y²= 4 and outside the circle x²+y²= 8. Set up (do not evaluate) a polar double integral equal to the mass of this lamina if the density at each point (x, y) is given by δ(x, y) = x²

Answer 1

x = rcosθ; y = rsinθ, dxdy = rdrdθ;

Mass m = ∫∫_Dx²dxdy; D: 2√2 ≤ r ≤ 4cosθ; - π/4 ≤ θ ≤π/4.

So, m = ∫_-π/4^π/4⌈_2√2^4cosθr³cos²θdrdθ