Solution
= Solution
{c}
A <parametrization> of the cylindrical patch is
$$
\mathbf r(x,\theta)=(x,2\cos\theta,2\sin\theta),\qquad
0<\theta<\pi/2,\quad0<x<2\cos\theta.
$$
The last range uses the planes $x=0$ and $x=y$. The <surface area element> is $|\mathbf r_x\times\mathbf r_\theta|\,dx\,d\theta=2\,dx\,d\theta$. Hence
$$
\boxed{A=\int_0^{\pi/2}\int_0^{2\cos\theta}2\,dx\,d\theta=4.}
$$
Including or excluding the boundary curves does not change the <surface area>.