The problem states: The base of a solid is the region bounded by the parabolas y=x^2 and y=2-x^2. Find the volume of the solid if the cross-section perpendicular to the x-axis are squares with one side lying along the base.
Here is what I did: x^2=2-x^2 (x-1)(x+2)= 0 x=1 , x=-2
pi *integral from -1 to 1 ((2-x^2)^2 - (x^2)^2 dx
pi*integral from -1 to 1(4-4x^2)dx
pi(4x - 4/3x^3) from limits -1 to 1 volume = 8pi
Is this procedure correct?