Problem

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Figure 1 shows the curve with equation

$$y=\ln\left(\tanh\frac x2\right)\qquad 1\le x\le 2$$

(a) Show that the length, $s$, of the curve is given by

$$s=\int_1^2 \coth x\,dx$$

(b) Hence show that

$$s=\ln\left(e-\frac1e\right)$$