Chapter 14.4, Problem 57ES

Use a CAS to graph the pseudosphere

$\begin{array}{l}x=\cos u\sin v\\ y=\sin u\sin v\\ z=\cos v+\ln \left(\tan \frac{v}{2}\right)\end{array}$

for $0\le u\le 2\pi ,0<v<\pi$ (see the accompanying figure), and then use the numerical double integration operation of the CAS to approximate the surface area between the planes $z=-1\text{and}z=1.$