定积分 （a^2 - x^2）^(1/2) 范围是0到2/π （π是圆周率）

let
x = asinb
dx = acosb db
x=0, b=0
x=π/2, arcsin(π/(2a))
∫(0,π/2)（a^2 - x^2）^(1/2) dx
= ∫(0,arcsin(π/2a)) a^2(cosb)^2 db
= (1/2)∫(0,arcsin(π/2a)) a^2(1+cos2b) db
= (a^2/2)[b+sin2b/2] (0,arcsin(π/(2a)))
= (a^2/2) [ arcsin(π/(2a)) + (π(4a^2-π^2)^(1/2)/(4a^2)) ]

!!!

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