- In this question you must show all stages of your working.
\section*{Solutions based on calculator technology are not acceptable.}
- Use integration by parts to find the exact value of
$$\int _ { 0 } ^ { 4 } x ^ { 2 } \mathrm { e } ^ { 2 x } \mathrm {~d} x$$
giving your answer in simplest form.
- Use integration by substitution to show that
$$\int _ { 3 } ^ { \frac { 21 } { 2 } } \frac { 4 x } { ( 2 x - 1 ) ^ { 2 } } \mathrm {~d} x = a + \ln b$$
where \(a\) and \(b\) are constants to be found.