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Let D a domain in R 2 define as follows, D := (x, y) 0 ≤...

Let D a domain in R 2 define as follows, D := (x, y) 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x ≤ 2y, y ≤ 2x . (1) Find the center of mass of D with respect to the following density function ρ,

ρ(x, y) = (x − (y/ 2) )^2 ((− x /2) + y)^2 ( x/2 + y/2 )^ 2 .

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