Step $2$

Simpson's Rule says that

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$~~$S_n$

$S_n=\frac{x}{3}[f(x_0)+4f(x_1)+2f(x_2)+$dots$+2f(x_n-2)+4f(x_n-1)+f(x_n)]$

We will use the table to find values for $v(t).$ For example, when $t=1\mathrm{.}5,$ we have

$v(1\mathrm{.}5)=,\frac{m}{s}$

Tutorial Exercise

A radar gun was used to record the speed of a runner during the first $5$ seconds of a race $($see the table$).$ Use Simpson's Rule to estimate the distance the runner covered during those $5$ seconds.

$\backslash$table$[[t(s),v(\frac{m}{s}),t(s),v(\frac{m}{s})$