1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{280ae2a5-7344-4ba3-907f-235fba3fd5b3-02_684_767_274_589}
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\caption{Figure 1}
\end{figure}
Figure 1 shows part of the curve with equation \(y = \sqrt { } \left( 0.75 + \cos ^ { 2 } x \right)\). The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(y\)-axis, the \(x\)-axis and the line with equation \(x = \frac { \pi } { 3 }\).
- Complete the table with values of \(y\) corresponding to \(x = \frac { \pi } { 6 }\) and \(x = \frac { \pi } { 4 }\).
| \(x\) | 0 | \(\frac { \pi } { 12 }\) | \(\frac { \pi } { 6 }\) | \(\frac { \pi } { 4 }\) | \(\frac { \pi } { 3 }\) |
| \(y\) | 1.3229 | 1.2973 | | | 1 |
- Use the trapezium rule
- with the values of \(y\) at \(x = 0 , x = \frac { \pi } { 6 }\) and \(x = \frac { \pi } { 3 }\) to find an estimate of the area of \(R\). Give your answer to 3 decimal places.
- with the values of \(y\) at \(x = 0 , x = \frac { \pi } { 12 } , x = \frac { \pi } { 6 } , x = \frac { \pi } { 4 }\) and \(x = \frac { \pi } { 3 }\) to find a further estimate of the area of \(R\). Give your answer to 3 decimal places.
(6)
\section*{LU}