(a)[4]
Evaluate $\int (\sin x - \cos x)^2 \, dx$.
(b(i))[3]
Estimate the value of $\int_{\frac{1}{4}\pi}^{\frac{1}{2}\pi} \cosec x \, dx$ by applying the trapezium rule with 2 intervals, and give your answer correct to 3 decimal places.
(b(ii))[2]
With the aid of a sketch of $y = \cosec x$ for $0 < x \leq \frac{1}{2}\pi$, explain whether the trapezium rule in part (i) gives an under-estimate or an over-estimate of the true integral value.