The height is given by the equation y = e^{x}. The area of a square is given by x ·y. Since the crosssections 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^{2x}dx 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}  e^{0}] = 1/2 [ e^{6} 1] = +1/2[1  e^{6}]
[1  e^{6}]/2
Jan 28

Lori C.
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