"Suppose you have the surface $z=3xy$ and you want to find the area that lies within the cylinder $x^2+y^2\leq 1$.
My homework is forcing me to use the parameterization
$\textbf{r}_1(s,t)= $
I am having a difficult time visualizing this parameterization, and I do not have any graphing software to graph the surface, but I want to make sure I understand this concept.
This is quite obvious, but I want to be sure; using the above parameterization, I am not parameterizing the entire surface, right? If I wanted to, I assume the parameterization would be $\textbf{r}_2(s,t) = $
Instead, is $\textbf{r}_1$ just the parameterization adjusted for the region - the region being the cylinder $x^2+y^2\leq 1$? That is, are we just making a revolution around $z=3xy$?
