The diagram shows part of the curve $y = e^{\left(-\frac{1}{2}x + 2\right)} + x - 1$ that intersects the $y$-axis at $R$. The tangent to the curve at $P(4, 4)$ intersects the $y$-axis at $Q$. Show that the area of the shaded region can be expressed as $ae^2 + b$ where $a$ and $b$ are constants to be determined. (Continuation of working space for question 11.)