The base of s is the region enclosed by the parabola y = 4 − 2x2 and the x−axis. cross-sections perpendicular to the y−axis are squares. find the volume

The length of each cross-section is determined by the horizontal distance (parallel to the x-axis) from one end of the parabola to the other.



which means this horizontal distance is



The area of each cross-section is simply the square of the section's side length, so the area would be .

So the volume of the solid would be