The height is given by the equation y = e-x. The area of a square is given by x ·y. Since the cross-sections are squares, the height and width will be the same. So the area of each individual square is (e-x)2 = e-2x.
To find the volume, add up all the infinitely thin squares from x = 0 to x = 3. The equation looks like
V = ∫e-2xdx where the limits of integration are x = 0 to x = 3.
Integrating, we get -(1/2) e-2x. Now if we use the limits, -1/2 [ e-6 - e0] = -1/2 [ e-6 -1] = +1/2[1 - e-6]
[1 - e-6]/2