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**Glitch** **The question:**

An electrical signal S(t) has its amplitude |S(t)| tested (sampled) every 1/10 of a second. It is desired to estimate the energy over a period of half a second, given exactly by:

$\displaystyle (\int_0^\frac{1}{2} \! |S(t)|^2 \, \mathrm{d}t)^{\frac{1}{2}}$

The result of the measurement are shown in the following table:

$\displaystyle \begin{center}

\begin{tabular}{| l | c | c| c| c| c|}

\hline

t & .1 & .2 & .3 & .4 & .5\\ \hline

\| S(t) \| & 60 & 50 & 50 & 45 & 55 \\ \hline

e(t) & 5 & 3 & 7 & 4 & 10 \\

\hline

\end{tabular}

\end{center}$

a) Using the above data for S(t), set up the appropriate Riemann sum and compute an appropriate value for the energy.

**My attempt:**

The set P (set of partitions) is clearly equal to {0, 1/10, 1/5, 3/10, 4/10, 1/2} so dt is 1/10 i.e. the width of each rectangle is 1/10.

My problem is with producing lower and higher Riemann sums. I'm used to having a function defined as something like $\displaystyle x^2$ and producing a general sum given dx (in this case, dt). In this question, we don't know the function, we're just given values.

Does this mean I take the max/min of each interval (e.g. [0, 1/10], [1/10, 1/5] etc.) and work out the partitions by hand? I'm a bit confused.

Any help would be greatly appreciated!