Compute the moments??

Question

M(sub x) = ∫∫(sub R) y dxdy

M(sub y) = ∫∫(sub R) x dxdy

where R is the region bounded by the ellipse:

[(x-8)^2]/4 + [(y-1)^2]/36 = 1

M(sub x) =

M(sub y) =

Answer 1

use a parametrization, polar coordinates

x = 2cos(t)

y = 6sin(t)

0 ≤ t ≤ 2π

don't forget dx dy = r dr dt