The diagram shows part of the graph of \(y=4e^{2x}+16e^{-2x}\), meeting the \(y\)-axis at the point \(A\) and the line \(x=1\) at the point \(B\).

(i) Find the coordinates of \(A\).

(ii) Find the \(y\)-coordinate of \(B\).

(iii) Find \(\displaystyle\int(4e^{2x}+16e^{-2x})\,dx\).

(iv) Hence find the area of the shaded region enclosed by the curve and the line \(AB\). You must show all your working.