How to find the area enclosed between two curves in 3-dimensions? I have two parametric equations, in 3-dimensions. I would like the find the area enclosed between them. How do I do this? 
I have looked at Line Integrals and these might be of use. However, I have no clue how to apply. 
To clarify: Take the area to be represented by an infinite number of lines drawn from corresponding $t$-values (since the curves are parametric).
New research: I have looked into Surface Integrals, seems the way to go as well.
Regards

As I mentioned in the comments, finding the minimal surface between two curves and integrating this is in general a hard problem and usually only numerically tractable (but some would probably disagree with that). If you want to see more, any search on 'minimal surfaces' should put you into some of the right places. I think, in some senses, a more interesting interpretation of the 'sheet' between the curves is the one formed by the minimum straight line distance (note that somewhat unintuitively this is not the minimal area surface). I only say this is more interesting because we can say more about it in general than the minimal area case. 
Let the two curves be denoted $C_1(s)$ and $C_2(s)$, where $s$ is an arclength parameter ranging between 0 and 1. We can always find this in theory (but not always in practice so maybe this isn't all that much more general). The surface we're after, say $\Sigma$, then is parametrized as 
\begin{equation}
\Sigma(s,t) = t C_1(s) + (1-t) C_2(s)
\end{equation}
and the surface area can be calculated as
\begin{equation}
AREA = \displaystyle \int_0^1 \int_0^1 \left\| \frac{\partial \Sigma(s,t)}{\partial s} \times \frac{\partial \Sigma(s,t)}{\partial t} \right\| ds dt
\end{equation}
which can almost certainly be simplified a lot but I'll just leave it there. 
