Answer
$\dfrac{64}{15}$
Work Step by Step
The point of intersection gives results: $2-x^2=x^2 \implies 2=2x^2 \\ \implies x =\pm 1$
Therefore, the volume of a solid can be computed as:
$V=\int_a^b A(y) dy=\int_{-1}^1 4(1-x^2)^2 \ dx \\=8 \int_0^1 (1-2x^2+x^4) \ dx \\= 8[x-\dfrac{2}{3}x^3+\dfrac{x^5}{5}]0^1 \\=8[1-\dfrac{2}{3}(1)+\dfrac{1}{5}\\=\dfrac{64}{15}$
