2 Fig. 2 shows the curve \(y = \sqrt { 1 + x ^ { 2 } }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c149cb5-7392-4219-b285-486f4694aa6f-2_574_944_612_598}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
- The following table gives some values of \(x\) and \(y\).
| \(x\) | 0 | 0.25 | 0.5 | 0.75 | 1 |
| \(y\) | 1 | 1.0308 | | 1.25 | 1.4142 |
Hence show that, using the trapezium rule with four strips, the shaded area is approximately 1.151 square units. - Jenny uses a trapezium rule with 8 strips, and obtains a value of 1.158 square units. Explain why she must have made a mistake.
- The shaded area is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. Find the exact volume of the solid of revolution formed.