Sure! To find the volume of the solid whose base is the region bounded by the curve y = x^2 and the x-axis from x = 0 to x = 2 and whose cross sections taken perpendicular to the x-axis are squares, we can use the following integral:
V = ∫[0,2] (x^4) dx
This is because each square cross section has an area of (side length)^2, and since each side length is equal to the height of the function (which is x^2), the area of each square is (x^2)^2 = x^4.
Evaluating this integral, we get:
V = [(1/5) x^5] from 0 to 2
V = (1/5) (2^5 - 0)
V = (1/5) (32) = 6.4
Therefore, the volume of the solid in question is 6.4 cubic units.