Problem

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

(i) Show that

$$\int_4^{4\sqrt3} \frac{8}{16+x^2}\,dx = p\pi$$

where $p$ is a rational number to be determined.

(ii) Determine the exact value of $k$ for which

$$\int_{3/4}^{k}\frac{2}{\sqrt{9-4x^2}}\,dx=\frac{\pi}{12}$$