(a) Use the Midpoint Rule with $n$ = 4 and the given data in the table below to estimate the value of the integral $\int_{0}^{\,3.2} {f(x)}\,dx.$ Make sure your answer is correct to two decimal places. $$\begin{array}{|c|c|}\hline {\it x} & {\it f}\,({\it x}) \\ \hline 0.0 & 6.8 \\ \hline 0.4 & 6.5 \\ \hline 0.8 & 6.3 \\ \hline 1.2 & 6.4 \\ \hline 1.6 & 6.9 \\ \hline 2.0 & 7.6 \\ \hline 2.4 & 8.4 \\ \hline 2.8 & 8.8 \\ \hline 3.2 & 9.0 \\ \hline \end{array}$$

$M_4 =$

(b) If it is known that $-4 \le f''(x) \le 1$ for all $x$, estimate the error involved in the approximation in part (a). Give your answer correct to four decimal places.

Error estimate: