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$\begingroup$

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

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:

Graph of the points

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?

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    http://www.math.lsa.umich.edu/courses/116/TeamHw/TeamHw3/TeamHw3.pdf Please don't answer questions like this...2012-02-03

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