Answer
$$\dfrac{53}{20}$$
Work Step by Step
$$Volume =\int_{0}^{1} \int_{y+1}^{4-2y} x^2y dx \space dy \\=\int_{0}^{1} \dfrac{x^3y}{3}|_{y+1}^{4-2y} dy \\=\int_0^1 (\dfrac{y}{3}) \times [(4-2y)^3-(y+1)^3] dy \\=\int_0^1 [-3y^4+15y^3-33y^2+21 y] dy\\=\dfrac{-3y^5}{5}+\dfrac{15y^4}{4}-11y^3+\dfrac{21y^2}{2}|_0^1\\ =\dfrac{53}{20}$$
