Получаем, что
V = int (0 1) dx int (x 1) dy int (0 x^2 + 2 * y^2) dz =
= int (0 1) dx int (x 1) dy (z)_{0}^{x^2 + 2 * y^2} =
= int (0 1) dx int (x 1) (x^2 + 2 * y^2) dy =
= int (0 1) dx (x^2 * y + 2/3 * y^3)_{x}^{1} =
= int (0 1) dx ((x^2 * 1 + 2/3 * 1^3) - (x^2 * x + 2/3 * x^3)) =
= int (0 1) (x^2 + 2/3 - x^3 - 2/3 * x^3) dx =
= int (0 1) (2/3 + x^2 - 5/3 * x^3) dx =
= (2/3 * x + 1/3 * x^3 - 5/3 * 1/4 * x^4)_{0}^{1} =
= (2/3 * x + 1/3 * x^3 - 5/12 * x^4)_{0}^{1} =
= (2/3 * 1 + 1/3 * 1^3 - 5/12 * 1^4) - (2/3 * 0 + 1/3 * 0^3 - 5/12 * 0^4) =
= 1 - 5/12 = 7/12.
Ответ: V = 7/12.