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\newcommand{\ds}{\displaystyle}
\newcommand{\un}{\underline}
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{\bf Question}

The table gives the velocity $v ms^{-1}$ of an electric milk float
$t$ seconds after starting from rest.

\begin{tabular} {|c|c|c|c|c|c|c|c|}
\hline

$t$ & 0 & 2 & 4 & 6 & 8 & 10 & 12\\

\hline

$v$ & 0 & 3.0 & 4.7 & 5.8 & 6.6 & 7.1 & 7.3\\

\hline
\end{tabular}

Use Simpson's rule to estimate the distance travelled in 12
seconds.
\medskip

{\bf Answer}

Now distance travelled in time $T$, $S=\ds\int_0^Tv \,dt$

Here $T=12$ and we have 7 ordinates $y_1 \rightarrow y_7$ and from
table the spacing of $x$ values gives $h=2$

$\begin{array} {rcl} S & = & \ds\frac{2}{3}
\times(\underbrace{0+7.3}+4(\underbrace{3.0+5.8+7.1})+2(\underbrace{4.7+6.6}))\\
& & \ \ \ \ \ \ \ \ y_1+y_7 \ \ \ \ \ \ \ \ y_2+y_4+y_6 \ \ \ \ \
\ \ \ \ \ y_3+y_5\\ & = & \un{62.333=62m} \rm{to\ 3s.f.}
\end{array}$
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