\section{Do not use a calculator in answering this question.}

It is given that $f(x)=2-\sin 4 x$.

(i) Find $\int f(x) d x$

[1]

(ii) Find the exact value, in terms of $\pi$, of $\int_{0}^{\frac{1}{2} \pi} x \mathrm{f}(x) \mathrm{d} x$.

[4]

(iii) Find the exact value, in terms of $\pi$, of $\int_{0}^{\frac{1}{2} \pi}(f(x))^{2} \mathrm{~d} x$.

[4]