Find the area of the surface given by $0 \leq x \leq 1$, $y=2x$, $z= e^{x+y}$.

Question

Im trying to parametrize the surface in order to propose an integral to find the area. However, Im not sure about how to set the limits of $u$ and $v$. This is my attempt: $x=u$, $y=v$, $z= e^{u+v}$, where $0 \leq u \leq 1$ and $0 \leq v \leq 2$. Is this okay? Or should I change it for $0 \leq v \leq 2x$?

Answer 1

$x = t, y = 2t, z = e^{3t},\\ \int_0^1 e^{3t} \sqrt {\frac {dx}{dt}^2 + \frac {dy}{dt}^2}\ dt$