- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Determine
$$\int \frac { 1 } { \sqrt { 5 + 4 x - x ^ { 2 } } } d x$$
- Use the substitution \(x = 3 \sec \theta\) to determine the exact value of
$$\int _ { 2 \sqrt { 3 } } ^ { 6 } \frac { 18 } { \left( x ^ { 2 } - 9 \right) ^ { \frac { 3 } { 2 } } } \mathrm {~d} x$$
Give your answer in the form \(A + B \sqrt { 3 }\) where \(A\) and \(B\) are constants to be found.