The base of a solid is a square with vertices (1,0), (0,1), (0, -1), and (-1, 0). Each cross-section perpendicular to the x-axis is a semi-circle. Find the volume.
I was attempting to find a quarter of the volume and just multiply by 4. I found the line above the x-axis to be y = 1-x, so attempting to use that, i came up with
8pi * Integral (1-x^2)(1-x) dx
I don't think this is right...