переходим к полярным координатам:
[m]x= ρ cos θ [/m]
[m]y= ρsin θ [/m]
Область D:
[m]4 ≤ ρ ≤ 5[/m]
[m]\frac{π}{2} ≤ θ ≤ π[/m]
[m]d σ =dxdy= ρ d ρ d θ [/m]
[m]m= ∫ ∫ _{ D }\frac{(-3 ρcos θ + ρsin θ )}{ ρ ^2} ρ d ρ d θ = ∫ ^{5}_{4} ( ∫^{π}_{\frac{π}{2} }(-3cos θ +sin θ )d θ )d ρ=[/m]
[m]=(-3sin θ-cos θ)| ^{π}_{\frac{π}{2}} ∫^{5}_{4} d ρ =(-3sinπ-cosπ+3sin \frac{π}{2}+cos \frac{π}{2})(5-4)=3-(-1)=4 [/m]