Question

Let phi (u,v)= (e^u cos v, e^u sin v, v) be a mapping from D= [0,1] x [0, pi] in the uv plane onto a surface S in xyz space.

Answer 1

\[\phi(u,v)=<e^u\cos{v},e^u\sin{v},v>\]
\[D=[0,1]\times[0,\pi]\]
Find the area of \[\phi(D)\]

Answer 2

\[T _{u}=<e ^{u}\cos{v},e^u\sin{v},0>\]
\[T _{v}=<-e^u\sin{v},e^u\cos{v},1>\]
\[||T _{u}\times T _{v}||=e^u \sqrt{1+e^{2u}}\]
so far this is where I got stucked