$ \begin{array}{rrrrrrrr} x & 0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 \\ f(x) & 2 & 1.3 & 0.9 & 0.6 & 0.7 & 1.1 & 1.9 \end{array} $
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:
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?