Complete the table of values for the curve \(y = \sqrt { \cos x }\).
\(X\)
0
\(\frac { \pi } { 8 }\)
\(\frac { \pi } { 4 }\)
\(\frac { 3 \pi } { 8 }\)
\(\frac { \pi } { 2 }\)
\(y\)
0.9612
0.8409
Hence use the trapezium rule with strip width \(h = \frac { \pi } { 8 }\) to estimate the value of the integral \(\int _ { 0 } ^ { \frac { \pi } { 2 } } \sqrt { \cos x } \mathrm {~d} x\), giving your answer to 3 decimal places.
Fig. 4 shows the curve \(y = \sqrt { \cos x }\) for \(0 \leqslant x \leqslant \frac { \pi } { 2 }\).
\begin{figure}[h]
State, with a reason, whether the trapezium rule with a strip width of \(\frac { \pi } { 16 }\) would give a larger or smaller estimate of the integral.