Answer
$\dfrac{63}{20}$
Work Step by Step
Consider $V= \int_{-2}^{1} \int_{x}^{2-x^2} x^2 dy dx$
or, $= \int_{-2}^{1} [x^2 y]_{x}^{2-x^2} dx$
or, $= \int_{-2}^{1} 2x^2-x^4-x^3 dx$
or, $= [ \dfrac{2x^3}{3}-\dfrac{x^5}{5}-\dfrac{x^4}{4}]_{-2}^{1}$
Thus, we have $I= [ \dfrac{2}{3}-\dfrac{1}{5}-\dfrac{1}{4}]- [ \dfrac{-16}{3}+\dfrac{32}{5}-\dfrac{16}{4}]=\dfrac{63}{20}$
