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Without getting into the whole question, I was asked to evaluate a surface integral

$\iint\limits_S f(x,y,z) da$

where S is the cylinder $x^2 + y^2 = x$ between $z=a$ and $z=b$

Now normally I would parametize this as a cylinder and it would be easy peasy but I'm worried about the equation of the cylinder, as my normal equation would be more like $x^2 + y^2 = C$ with C being some constant .. Any thoughts ? thanks a lot

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$x^2+y^2=x$ is the equation of a circle, get center and radius. – enzotib Aug 12 '12 at 14:48
up vote 4 down vote accepted

Your cylinder is offset from the axis. $x^2+y^2=x$ becomes $(x-\frac 12)^2+y^2=\frac 14$. You can substitute $u=x-\frac 12$ to get back on axis if you want.

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thanks boss .. concise and complete :) – Ronald Aug 12 '12 at 15:00

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