Use the function y = 2^{x}to find the function values.

These are all nice points above the x-axis, so they are effectively radii of circles, once the curve is rotated around the x-axis.

So, now you can find the area of these three circles since you know the radii!

Area circle 1 = πr^{2}= π x (2^{1})^{2}= 4π

Area circle 2 = πr^{2}= π x (2^{1.5})^{2}= 8π

Area circle 3 = πr^{2}= π x (2^{2})^{2}= 16π

Rather than use Simpson's Rule to find the area, use it to find the volume.

Volume = h/3 x (A_{1}+ 4A_{2}+ A_{3})

= 0.5/3 x (4π + 4 x 8π + 16n)

= 0.5/3 x 52π

= 27.227136333

= 27.2 cubic units

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