>252
　-√(x-x^2) ≦ y ≦ √(x-x^2),
　∫[-√(x-x^2), √(x-x^2)] dy = 2√(x-x^2) = 2(√x)√(1-x),
　∫2x√(1-x) dx = ∫{2√(1-x) - 2(1-x)^(3/2)}dx = -(4/3)(1-x)^(3/2) + (4/5)(1-x)^(5/2),
　0≦x≦1 で積分すれば (4/3) - (4/5) = 8/15.