The third component of the normal vector is-1, and hutcheson d is x 2+y 2.
Origin = double integral _ (d) x 2 * y 2 * (root (r 2-x 2-y 2)) * (-1) dxdy.
Note that the last formula-1 is due to low demand.
Polar coordinates X = rcosa, Y = rsina Jacobian is r,
= integral (from 0 to R) doctor integral (from 0 to 2pi music) r 4 * cos 2a * sin 2a root (r 2-r 2) RDA
On the indivisible whole (music from 0 to 2pi) (1 cos4a)/ 8 =π/ 4.
Integral of variable substitution = Sina, 0
Integral (from 0 to π/ 2) sin 5a * cos 2ada
=1/3-2/5+1/7 = 8/105, finally.
= 2pi/ 105 .