Explain this to me!
the base of a solid in the region bounded by the graphs of y = e-x y = 0, and x = 0, and x = 1. cross sections of the solid perpendicular to the x-axis are semicircles. what is the volume, in cubic units, of the solid?

I've attached a plot of one such cross section (grayish orange) with its diameter lying in the region (blue) bounded above by the curve (red). (This cross section is taken at .)

The area of each cross section in terms of its diameter is , where the diameter is determined by the vertical distance (in the x-y plane) between the curve and the x-axis . So, .

The volume would then be