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\includegraphics[max width=\textwidth, alt={}, center]{5b5ed7d1-028e-4f9a-ae9e-26071d0df678-14_604_497_262_822}
The diagram shows the graph of \(y = \sec x\) for \(0 \leqslant x < \frac { 1 } { 2 } \pi\).
- Use the trapezium rule with 2 intervals to estimate the value of \(\int _ { 0 } ^ { 1.2 } \sec x \mathrm {~d} x\), giving your answer correct to 2 decimal places.
- Explain, with reference to the diagram, whether the trapezium rule gives an overestimate or an underestimate of the true value of the integral in part (i).
- \(P\) is the point on the part of the curve \(y = \sec x\) for \(0 \leqslant x < \frac { 1 } { 2 } \pi\) at which the gradient is 2 . By first differentiating \(\frac { 1 } { \cos x }\), find the \(x\)-coordinate of \(P\), giving your answer correct to 3 decimal places.