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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 3}\quad {\sl Sept. 14, 1995}

\begin{enumerate}
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\item Define the following:

  \begin{enumerate}[a)]
  \item A step function $s$ on $[a,b]$.
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  \item $\int_a^b s(x)\,dx$ where $s$ is a step function on $[a,b]$.
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  \item $\int_a^b f(x)\,dx$ where $f$ is a bounded function on $[a,b]$.
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  \end{enumerate}

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\item State and prove the Linearity Property for integrals of step
functions.
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\item Let $s$ and $t$ be step functions such that
$\int_{-1}^3 s(x)dx = 2$ and \mbox{$\int_0^1 t(x)dx = 3$}.
Determine the value of $\int_{0}^4 5s(x-1) + t(x/4)\,dx$. (Justify your
steps).

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