Recent content by dbkats

Homework Statement Let C be a cylinder of radius 1. It is cut by the x-y plane from below, and by the plane z-x=1 above. Parametrize all the surfaces of the cylinder. Find a unit normal (pointing outward) for each surface. Homework Equations Equation for a cylinder: x^2+y^2=1 Equation of the...

Or that, you hahaha...

>.< I feel silly. The integrand evaluates to -1, so I can now use whatever parametrization I feel like. I think that (x-2)=cosθ, (y-3)=sinθ would be a good bet. I guess once I saw the disk, all I could think about was "how am I going to parametrize this ugly thing"... Anyway, thanks so...

So, I actually messed up writing it out here. It should actually be: Integrand = (2/(1 + (x/y)2))-1-(2y/(x2+y2)) I feel very stupid for not seeing that it drastically simplifies when I work out the common denominator. Integrand = (y2 - 2y - x2)/(x2 + y2) Barring any other stupid arithmetic...

I feel that the conventional polar coordinates will not do well because the disk is not centered at the origin. So when we transform the disk region, we do not get a nice square. Or did I misunderstand how that works? My integral with respect to x and y: 2∫13dx∫3√(1-(x-2)2)+3{(2/(1 +...

Use Green's THM to calculate the line integral ∫C(F<dot> dx), where C is the circle (x-2)2 + (y - 3)2=1 oriented counterclockwise, and F(x,y)=(y+ln(x2+y2), 2tan-1(x/y)). Green's THM ∫∂SF<dot>dx=∫∫S(∂F2/∂x) - ∂F1/∂y) I tried doing it by brute force. I took the partials and put them...