The figure shows part of the curve $y = g(x)$. $(2, 8)$ and $(6, 1)$ are two points on the curve. Given that $\int_{2}^{6} y \text{ } dx = 32$, find the value of $\int_{1}^{8} x \text{ } dy$. The diagram shows part of the curve $y = e^x$. The normal to the curve at point $A$ where $x = 1$ intersects the $x$-axis at point $B$. Find the area of the shaded region. Leave your answer in exact form.