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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 5}\quad {\sl Oct.\ 5, 1995}

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\item A rod of length $L$ is placed on the $x$-axis with one end on the origin.
Suppose the rod has a mass density function given by $\rho(x) = L^2 - x^2$.
Compute the center of mass of the rod.

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\item Prove that $\sin^2(x) = \frac{1-\cos(2x)}{2}$ and
$\cos^2(x) = \frac{1+\cos(2x)}{2}$. (Use the addition formulas).

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\item Sketch the graph of the function $F(x) = \int_0^x |t|\,dt$ for $-2
\le x \le 2$.
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