?(a) A table of values of a function \(g\) is given. Use Simpson's Rule to
Chapter 7, Problem 32(choose chapter or problem)
(a) A table of values of a function \(g\) is given. Use Simpson's Rule to estimate
\(\int_{0}^{1.6} g(x) d x\)
\(\begin{array}{|c|c||c|c|}
\hline x & g(x) & x & g(x) \\
\hline 0.0 & 12.1 & 1.0 & 12.2 \\
0.2 & 11.6 & 1.2 & 12.6 \\
0.4 & 11.3 & 1.4 & 13.0 \\
0.6 & 11.1 & 1.6 & 13.2 \\
0.8 & 11.7 & & \\
\hline
\end{array}\)
(b) If \(-5 \leqslant g^{(4)}(x) \leqslant 2 \text { for } 0 \leqslant x \leqslant 1.6\), estimate the error involved in the approximation in part (a).
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