>>75
0≦x≦1/y^2で積分してみると

∫ (1-x y^2)^(1/2) dx = [ -(2/3)(1/y^2) (1- x y^2)^(3/2) ] = (2/3)(1/y^2) になる
これを
y ≧1で積分すれば
∫(2/3) (1/y^2) dy = (2/3) [ -(1/y) ] = (2/3)