3
\includegraphics[max width=\textwidth, alt={}, center]{b4a4082c-f3cd-47c5-8673-680dae9a22bd-04_684_455_260_845}
The diagram shows the curve \(y = 2 + \mathrm { e } ^ { - 2 x }\). The curve crosses the \(y\)-axis at the point \(A\), and the point \(B\) on the curve has \(x\)-coordinate 1 . The shaded region is bounded by the curve and the line segment \(A B\).
Find the exact area of the shaded region.