I have read a lot about this on MSE before, but all simply briefly mention the possibility of doing it through line integrals and double integrals. But none of have actually explained in detail how it is done.
If we have the equations of two intersecting perpendicular cylinders, let's say $x^2+y^2=1$ and $z^2+y^2=1$, how does one go about parametrizing in such a way that a double integral can be taken that gives the surface area? I would be appreciate if it was laid out as I can't visually come up with a way to parametrize it.
In addition, how would one use a line integral to calculate this? I assume you would utilize Stokes's Theorem but other than that I am not knowledgable enough to attempt this.
Thank you.