int (0 1) (1 - y) * (2 * y^(1/2) - y^(1/2)) dy =
= int (0 1) (1 - y) * y^(1/2) dy =
= int (0 1) (y^(1/2) - y^(3/2)) dy =
= (1/(1/2 + 1) * y^(1/2 + 1) - 1/(3/2 + 1) * y^(3/2 + 1))_{0}^{1} =
= (2/3 * y^(3/2) - 2/5 * y^(5/2))_{0}^{1} =
= 2/3 * 1^(3/2) - 2/5 * 1^(5/2) = 2/3 - 2/5 = 10/15 - 6/15 = 4/15.