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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.

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    what do you mean "compute the surface"? Do you want its area?2012-07-23
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    Do 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
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    Yes I want the area, I just fixed it. Thank you for pointing it out.2012-07-23
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    $z=xy$ 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
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    @joriki yes I do2012-07-23

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