Use the change of variables $x=r \cosh \theta, y=r \sinh \theta$ to evaluate

$$\int_{A} y d x d y$$

where $A$ is the region of the $x y$-plane bounded by the two line segments:

$$\begin{aligned} &y=0, \quad 0 \leqslant x \leqslant 1 \\ &5 y=3 x, \quad 0 \leqslant x \leqslant \frac{5}{4} \end{aligned}$$

and the curve

$$x^{2}-y^{2}=1, \quad x \geqslant 1$$