大圆y=3-√(9-x²) 小圆y=√[2.25-(x-1.5)²]
交点x=2.4
S=∫(0,2.4)√[2.25-(x-1.5)²]dx-∫(0,2.4)[3-√(9-x²)]dx
=∫(0,2.4)1.5√[1-(x-1.5)²/1.5²]dx-∫(0,2.4)3dx+∫(0,2.4)3√(1-x²/3²)]dx
令(x-1.5)=1.5sint₁→dx=1.5cost₁dt₁ 积分限→-π/2,arcsin(0.6)
x=3sint₂→dx=3cost₂dt₂ 积分限→0,arcsin(0.8)
S=∫(-π/2,arcsin(0.6) )1.5cost₁·1.5cost₁dt₁-7.2+∫(0,arcsin(0.8))3cost₂]3cos₂tdt₂
=1.5²∫(-π/2,arcsin(0.6))½(cos2t₁+1)dt₁+3²∫(0,arcsin(0.8))½(cos2t₂+1)dt₂-7.2
=1.5²·(¼sin2t₁+½t₁)|(-π/2,arcsin(0.6))+3²·(¼sin2t₂+½t₂)|(0,½)-7.2
=1.5²[0.24+½arcsin(0.6)+π/4]+9·[0.24+½arcsin(0.8)]-7.2
≈2.163913096