- (a) Given that
$$y = \ln \left( 3 + x ^ { 2 } \right)$$
complete the table with the value of \(y\) corresponding to \(x = 3\), giving your answer to 4 significant figures.
| \(\boldsymbol { x }\) | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |
| \(\boldsymbol { y }\) | 1.946 | 2.225 | | 2.725 | 2.944 | 3.146 | 3.332 |
In part (b) you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
(b) Use Simpson's rule with all the values of \(y\) in the completed table to estimate, to 3 significant figures, the value of
$$\int _ { 2 } ^ { 5 } \ln \left( 3 + x ^ { 2 } \right) \mathrm { d } x$$
(c) Using your answer to part (b) and making your method clear, estimate the value of
$$\int _ { 2 } ^ { 5 } \ln \sqrt { \left( 3 + x ^ { 2 } \right) } \mathrm { d } x$$