Let $S\subset \mathbb{R}^3$ be the surface enclosed by the (infinitely long) open cylinder in $\mathbb{R}^2$ (given by the equation $x^2+y^2<1$) and the surface $z=xy$. Explicitly, $S=\{(x,y,z): x^2+y^2<1\text{ and } z=xy\}$. How do I compute the area of $S$, by using a double integral.
cutting of a slice from a cylinder
1
$\begingroup$
calculus
integration
multivariable-calculus
-
1what do you mean "compute the surface"? Do you want its area? – 2012-07-23
-
0Do you know a formula for the surface area involving partial derivatives? If you do, the problem is straightforward (especially in cylindrical coordinates). – 2012-07-23
-
0Yes I want the area, I just fixed it. Thank you for pointing it out. – 2012-07-23
-
0$z=xy$ is a surface, not a curve. The set $S=\{(x,y,z): x^2+y^2<1\text{ and } z=xy\}$ is the part of the surface $z=xy$ that is inside the cylinder $x^2+y^2\lt1$. Is that what you mean? – 2012-07-23
-
0@joriki yes I do – 2012-07-23