>>777
∫[0,1](∫[-√(x-x^2),√(x-x^2)]√xdy)dx
=2∫[0,1]√(x-x^2)√xdx
=2∫[0,1]x√(1-x)dx
=-2∫[0,1]((1-x)-1)√(1-x)dx
=-2∫[0,1]((1-x)^(3/2)-(1-x)^(1/2))dx
=2[(2/5)(1-x)^(5/2)-(2/3)(1-x)^(3/2))]_[0,1]
=8/15