3.40: Area involving a tangent to a reciprocal-power curve

The diagram shows part of the curve $y = \left(4x + 3\right)^{-\frac{1}{2}} + 1$ and the line $x = 9$. Point $A$ has $x$-coordinate $1$. The tangent at $A$ meets the $x$-axis at $B$. Find the area of the shaded region.