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f(x) 2 1.3 0.9 0.6 0.7 1.1 1.9

Find a formula for the volume V of the solid whose base is the region bounded by y = f(x), the x-axis, and the line x = 3 and its cross-sections perpendicular to the x-axis are semicircles.**

So, I plotted the points and got a graph that looks something like this:

http://i.imgur.com/AiFo6.jpg

Now to start on actually solving the problem.

So I figure that we should break the region up into a small dx pieces, and just sum up all of these pieces using an integral.

However, I'm having trouble figuring our what the area of each piece will be. Any help?