Let S be the solid with flat base, whose base is the region in the xy plane defined by the curves y=ex , y=−1 , x=1 and x=2 , and whose cross-sections perpendicular to the x axis are equilateral triangles with bases that sit in the xy plane.
a) Find the area A(x) of the cross-section of S given by the equilateral triangle that stands perpendicular to the x axis, at coordinate x .