x^2+y^2<=2y
x^2+y^2-2y+1<=1
x^2+(y-1)^2<=1
x+y>=2
如图
令x=pcosa y=psina
x^2+y^2<=2y
p^2<=2psina
p<=2sina
x+y=pcosa+psina=p(sina+cosa)>=2
p>=2/(sina+cosa)
x+y=2与 x^2+y^2=2y的交点(目的是求出a的范围)是
(1,1)与(0,2)
tana1=1/1=1 a1=π/4
tana2=2/0=∞ a2=π/2
∴积分化为
∫(π/4->π/2)da ∫(2/(sina+cosa) -> 2sina) pcosa*psina *pdp
=∫(π/4->π/2)sinacosa ∫(2/(sina+cosa) -> 2sina) p^3dp
下面自己去算吧
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