Given that \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ & $4.0$ & $4…

Previous year question for Numerical Methods & Transform Calculus.

Question

Given that

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

\hline

$x$ & $4.0$ & $4.2$ & $4.4$ & $4.6$ & $4.8$ & $5.0$ & $5.2$ \\

\hline

$\log x$ & $1.3863$ & $1.4351$ & $1.4816$ & $1.5261$ & $1.5686$ & $1.6094$ & $1.6487$ \\

\hline

\end{tabular}

evaluate $\int_{4}^{5.2} \log x \, dx$ by Trapezoidal rule and Simpson's $1/3$ rule.