Answer
$\dfrac{16}{3} \ square \ unit $
Work Step by Step
We have the area of a square is: $A(x)=(\ length)^2=(2x)^2=4x^2$
Now, the equation of a base yields: $y=x^2$
So, the area of a square becomes : $4y$
The volume of a solid can be computed as:
$V=\int_a^b A(y) dy=\int_0^1 (4y)^2 \ dy \\=16 [\dfrac{y^3}{3}]_0^1 \\=\dfrac{16}{3} \ square \ unit $
