7 A curve has equation \(y = 4 x \cos 2 x\).
- Find an exact equation of the tangent to the curve at the point on the curve where
$$x = \frac { \pi } { 4 }$$
- The region shaded on the diagram below is bounded by the curve \(y = 4 x \cos 2 x\) and the \(x\)-axis from \(x = 0\) to \(x = \frac { \pi } { 4 }\).
\includegraphics[max width=\textwidth, alt={}, center]{b8614dd6-2197-40c3-a673-5bef3e3653a5-8_487_878_740_591}
By using integration by parts, find the exact value of the area of the shaded region.
(5 marks)
\includegraphics[max width=\textwidth, alt={}]{b8614dd6-2197-40c3-a673-5bef3e3653a5-8_1275_1717_1432_150}