Find \(\int ( \sin x - \cos x ) ^ { 2 } \mathrm {~d} x\).
Use the trapezium rule with 2 intervals to estimate the value of
$$\int _ { \frac { 1 } { 4 } \pi } ^ { \frac { 1 } { 2 } \pi } \operatorname { cosec } x d x$$
giving your answer correct to 3 decimal places.
Using a sketch of the graph of \(y = \operatorname { cosec } x\) for \(0 < x \leqslant \frac { 1 } { 2 } \pi\), explain whether the trapezium rule gives an under-estimate or an over-estimate of the true value of the integral in part (i).